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SUMMARY:Strongly Correlated Quantum Materials and High-Temperature Superconductors Series
DESCRIPTION:In the 2020-2021 academic year\, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom. \nCuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator\, several fascinating phases emerge\, including a d-wave superconductor\, a pseudo-gap metal\, and strange metal. After intensive studies from experimental\, theoretical\, and numerical communities for more than three decades\, remarkable progress has been made\, but basic questions remain: \n\nWhat is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling\, spin fluctuations\, or resonating-valence-bonds?\nHow do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters\, or do we need an unconventional picture involving fractionalization?\nIs the strange metal at optimal doping associated with a quantum critical point? And if so\, what is the driving force of this phase transition?\n\nThe cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics\, such as quantum spin liquids\, topological order\, and non-Fermi liquids. In the coming years\, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series\, we hope to accelerate this process by bringing together deeper conversations between experimental\, theoretical\, and numerical experts with different backgrounds and perspectives. \nThe Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar. \nSeminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard). \nScientific program advisors: Professor Subir Sachdev (Harvard)\, Professor Patrick Lee (MIT). \nIn order to learn how to attend this series\, please fill out this form. \nFor more information\, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu) \nSpring 2022\nApril 20\, 2022 | 11:30 – 1:00 pm ET \nHarold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory) \nTitle: Superconductivity in infinite-layer nickelates \nAbstract: Since its discovery\, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates\, observation of a doping-dependent superconducting dome\, and our current understanding of their electronic and magnetic structure. \n\nFebruary 3\, 2022 | 11:30 – 1:00 pm ET \nLu Li (U Michigan) \nTitle: Quantum Oscillations of Electrical Resistivity in an Insulator \nAbstract: In metals\, orbital motions of conduction electrons are quantized in magnetic fields\, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators\, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12\, despite much larger than that of usual metals\, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems. \n2020 – 2021\nSeptember 2\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nSubir Sachdev (Harvard) \nTitle: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders \nAbstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter\, often called the pseudogap metal\, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role\, at best\, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also\ndescribe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons\, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality\, both approaches have in common emergent fractionalized excitations\, and a significantly larger entropy than naively expected. \nVideo\n\n\n\n\nSeptember 23\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nSubir Sachdev (Harvard) \nTitle: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II \nAbstract: In this second talk\, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice\,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model\, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters\, obtained recently with Henry Shackleton\, Alexander Wietek\, and Antoine Georges. \nVideo\n\n\n\n\nSeptember 24\, 2020 | 12:00pm ET\n\n\n\n\n\n\n\nInna Vishik (University of California\, Davis)\n\nTitle: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c )\, and after more than three decades of extraordinary research activity\, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-\, temperature-\, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena\, both in terms of connecting multiple experimental techniques for a single material\, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video\n\n\n\n\nOctober 15\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nLouis Taillefer (Université de Sherbrooke) \nTitle: New signatures of the pseudogap phase of cuprate superconductors \nAbstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range\, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p\, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements\, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p\, where it varies in temperature as C el ~ – T logT. At p and just above\, the electrical resistivity is linear in T at low T\, with an inelastic scattering rate that obeys the Planckian limit. Finally\, the pseudogap phase is found to have a large negative thermal Hall conductivity\, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase. \nVideo\n\n\n\n\nOctober 28\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nPatrick Lee (MIT) \nTitle: The not-so-normal normal state of underdoped Cuprate \nAbstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations\, together with a variety of order such as charge order\, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave)\, a unified description of this phenomenology is possible. As an example\, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai\, Senthil\, Lee\, Phys Rev B101\, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices\, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave. \nVideo\n\n\n\n\nNovember 6\, 2020 |12:30pm ET\n\n\n\n\n\n\n\nZhi-Xun Shen (Stanford University) \nTitle: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors \nAbstract: High‐temperature superconductivity in cupper oxides\, with critical temperature well above what wasanticipated by the BCS theory\, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system\, yet extremely rich ‐ boasting d‐wave superconductivity\, pseudogap\, spin and charge orders\, and strange metal phenomenology. For this reason\, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model\, quantum critical point\, Planckian metal and beyond.\nCentral to this debate is whether the Hubbard model\, which is the natural starting point for the undoped\nmagnetic insulator\, contains the essential ingredients for key physics in cuprates. In this talk\, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First\, we show results that naturally points to the importance of Coulomb and magnetic interactions\, including d‐wave superconducting gap structure [4]\, exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second\, we evidence effects beyond the Hubbard model\, including band dispersion anomalies at known phonon frequencies [6\, 7]\, polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third\, we show properties likely of hybrid electronic and phononic origin\, including the pseudogap [9‐11]\, and the almost vertical phase boundary near the critical 19% doping [12]. Fourth\, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally\, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable\, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term\, likely of phononic origin\, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions\, and holon‐ holon attraction. Given the structural similarity of the materials\, It is likely that an extended two‐dimensional\n(2D) Hubbard model with such an attractive term\, will connect the dots of the above four classes of\nexperimental observables and provide a holistic understanding of cuprates\, including the elusive d‐wave superconductivity in 2D Hubbard model. \n[1] A. Damascelli\, Z. Hussain\, and Z.‐X. Shen\, Review of Modern Physics\, 75\, 473 (2003)\n[2] M. Hashimoto et al.\, Nature Physics 10\, 483 (2014)\n[3] JA Sobota\, Y He\, ZX Shen ‐ arXiv preprint arXiv:2008.02378\, 2020; submitted to Rev. of Mod. Phys.\n[4] Z.‐X. Shen et al.\, Phys. Rev. Lett. 70\, 1553 (1993)\n[5] B.O. Wells et al.\, Phys. Rev. Lett. 74\, 964 (1995)\n[6] A. Lanzara et al.\, Nature 412\, 510 (2001)\n[7] T. Cuk et al.\, Phys. Rev. Lett.\, 93\, 117003 (2004)\n[8] K.M. Shen et al.\, Phys. Rev. Lett.\, 93\, 267002 (2004)\n[9] D.M. King et al.\, J. of Phys. & Chem of Solids 56\, 1865 (1995)\n[10] D.S. Marshall et al.\, Phy. Rev. Lett. 76\, 484 (1996)\n[11] A.G. Loeser et al.\, Science 273\, 325 (1996)\n[12] S. Chen et al.\, Science\, 366\, 6469 (2019)\n[13] T.P. Devereaux\, T. Cuk\, Z.X. Shen\, N. Nagaosa\, Phys. Rev. Lett.\, 93\, 117004 (2004)\n[14] S. Johnston et al.\, Phys. Rev. Lett. 108\, 166404 (2012)\n[15] Yu He et al.\, Science\, 362\, 62 (Oct. 2018)\n[16] Z. Chen\, Y. Wang et al.\, preprint\, 2020 \nVideo\n\n\n\n\nNovember 12\, 2020 |10:30am ET\n\n\n\n\n\n\n\nChandra Varma (Visting Professor\, University of California\, Berkeley.\nEmeritus Distinguished Professor\, University of California\, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:\n1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.\n2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.\n3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.\n4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting\,\n(i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.\n(ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.\n(iii) Problems.Video\n\n\n\n\nNovember 18\, 2020 |10:30am ET\n\n\n\n\n\n\n\nAntoine Georges (Collège de France\, Paris and Flatiron Institute\, New York) \nTitle: Superconductivity\, Stripes\, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model? \nAbstract: Simplified as it is\, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk\, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt\, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method\, the community has recently embarked into a major effort to combine and critically compare these approaches\, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature\, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open\, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible\, connections to the physics of cuprate superconductors will be made. If time permits\, I may also address the question of Planckian transport and bad metallic transport at high temperature. \nVideo\n\n\n\n\nNovember 19\, 2020 |10:30am ET\n\n\n\n\n\n\n\nEduardo Fradkin (University of Illinois at Urbana-Champaign) \nTitle: Pair Density Waves and Intertwined Orders in High Tc Superconductors\n\nAbstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis. \nVideo\n\n\n\n\nNovember 25\, 2020 |10:30am ET\n\n\n\n\n\n\n\nQimiao Si (Rice University) \nTitle: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems \nAbstract: Strongly correlated electron systems often show bad-metal behavior\, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders\, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study\, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals\, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk\, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk\, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”\, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.\n\n\n\n\nDecember 2\, 2020 |10:30am ET\n\n\n\n\n\n\n\nAndrey Chubukov (University of Minnesota) \nTitle: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal \n\nAbstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm\, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes\, in particular\, the pairing at a 2D Ising-nematic critical point in (γ=1/3)\, a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins\, unless the pairing component of the interaction is artificially reduced\, but because of fermionic incoherence in the normal state\, the system develops a pseudogap\, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations\, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices\, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite\, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.\n\n\n\n\nDecember 9\, 2020 |10:30am ET\n\n\n\n\n\n\n\nDavid Hsieh (Caltech) \nTitle:  Signatures of anomalous symmetry breaking in the cuprates   \nAbstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking\, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular\, I will discuss our data on YBa2Cu3Oy [1]\, which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl2 [2]\, where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.\n[1] L. Zhao\, C. A. Belvin\, R. Liang\, D. A. Bonn\, W. N. Hardy\, N. P. Armitage and D. Hsieh\, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy\,” Nature Phys. 13\, 250 (2017). \n[2] A. de la Torre\, K. L. Seyler\, L. Zhao\, S. Di Matteo\, M. S. Scheurer\, Y. Li\, B. Yu\, M. Greven\, S. Sachdev\, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2\,” Preprint at https://arxiv.org/abs/2008.06516\n\n\n\n\nDecember 16\, 2020 |10:30am ET\n\n\n\n\n\n\n\nZheng-Yu Weng (Tsinghua University) \nTitle: Organizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors\n\nAbstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture\, an exact organizing principle for a typical doped Mott insulator will be presented\, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular\, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.\n\n\n\n\nDecember 17\, 2020 |10:30am ET\n\n\n\n\n\n\n\nSteven Kivelson (Stanford University) \nTitle: What do we know about the essential physics of high temperature superconductivity after one third of a century? \nAbstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding\, I will argue that the answer to the title question is “quite a lot.” To focus the discussion\, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure\, although from a perspective that differs from his in many key points.\n\n\n\n\nJanuary 20\, 2021 |10:30am ET\n\n\n\n\n\n\n\nThomas Peter Devereaux (Stanford University) \nTitle:  Numerical investigations of models of the cuprates\n\nAbstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach\, these people are the failures in this field. . . ” \nI will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods\, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models\, and then I will discuss “phases” of these models\, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.\n\n\n\n\nFebruary 3\, 2021 |10:30am ET\n\n\n\n\n\n\n\nPhilip Phillips (University of Illinois Urbana-Champaign) \nTitle: Beyond BCS: An Exact Model for Superconductivity and Mottness\n\nAbstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently\, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator\, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem\, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state\, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons\, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.\n[1] PWP\, L. Yeo\, E. Huang\, Nature Physics\, 16\, 1175-1180 (2020).\n\n\n\n\nFebruary 10\, 2021 |10:30am ET\n\n\n\n\n\n\n\nSenthil Todadri (MIT) \nTitle: Strange metals as ersatz Fermi liquids: emergent symmetries\, general constraints\, and experimental tests \nAbstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk\, I will discuss\, in great generality\, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many\, if not all\, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations\, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.\n[1]. Dominic Else\, Ryan Thorngren\, T. Senthil\, https://arxiv.org/abs/2007.07896\n[2]. Dominic Else\, T. Senthil\, https://arxiv.org/abs/2010.10523\n\n\n\n\nApril 1\, 2021 |9:00am ET\n\n\n\n\n\n\n\nNaoto Nagaosa (University of Tokyo) \nTitle: Applied physics of high-Tc theories \nAbstract: Since the discovery of high temperature superconductors in cuprates in 1986\, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially\, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk\, I would like to describe the development of RVB idea to broader class of materials\, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect\, spin Hall effect\, topological insulator\, multiferroics\, various topological spin textures\, e.g.\, skyrmions\, and nonlinear optics. I will show that even though the phenomena are extensive\, the basic idea is rather simple and common in all of these topics.\n\n\n\n\nApril 22\, 2021 |10:30am ET\n\n\n\n\n\n\n\nDung-Hai Lee (UC Berkeley) \nTitle: “Non-abelian bosonization in two and three spatial dimensions and some applications” \nAbstract: In this talk\, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications\, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model\, critical spin liquids of “bipartite-Mott insulators” in 1\,2\,3 spatial dimensions\, and twisted bilayer graphene.\n\n\n\n\nMay 12\, 2021 |10:30am ET\n\n\n\n\n\n\n\nAndré-Marie Tremblay (Université de Sherbrooke) \nTitle: A unified theoretical perspective on the cuprate phase diagram \nAbstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain\, at least qualitatively\, many of these features. More specifically\, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap\, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.\n\n\n\n\nAugust 11\, 2021 |10:30am ET\n\n\n\n\n\n\n\nPiers Coleman (Rutgers) \nTitle: Order Fractionalization* \nAbstract: I will discuss the interplay of spin fractionalization with broken\nsymmetry. When a spin fractionalizes into a fermion\, the resulting particle\ncan hybridize or pair with the mobile electrons to develop a new kind of\nfractional order parameter. The concept of “order fractionalization” enables\nus to extend the concept of off-diagonal order to encompass the formation of\nsuch order parameters with fractional quantum numbers\, such as spinorial\norder[1].\nA beautiful illustration of this phenomenon is provided by a model\nwhich incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This\nmodel explicitly exhibits order fractionalization and is expected to undergo a\ndiscrete Ising phase transition at finite temperature into an\norder-fractionalized phase with gapless Majorana excitations.\nThe broader implications of these considerations for Quantum\nMaterials and Quantum Field Theory will be discussed.\nWork done in collaboration with Yashar Komijani\, Anna Toth and Alexei\nTsvelik.\n[1] Order Fractionalization\, Yashar Komijani\, Anna Toth\, Premala Chandra\, Piers Coleman\, (2018).\n[2] Order Fractionalization in a Kitaev Kondo model\, Alexei Tsvelik and Piers Coleman\, (2021).\n\n\n\n\nSeptember 15\, 2021 |10:30am ET\n\n\n\n\n\n\n\nLiang Fu (MIT) \nTitle: Three-particle mechanism for pairing and superconductivity \nAbstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small\, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion\, I will show that two doped charges can attract and form a bound state\, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping\, including spin-triplet superconductivity\, pair density wave\, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials\, ZrNCl and WTe2 will be discussed. \n[1] V. Crepel and L. Fu\, Science Advances 7\, eabh2233 (2021)\n[2] V. Crepel and L. Fu\, arXiv:2103.12060\n[3] K. Slagle and L. Fu\,  Phys. Rev. B 102\, 235423 (2020)\n\n\n\n\nSeptember 29\, 2021 |11:30am ET (special time)\n\n\n\n\n\n\n\nNai Phuan Ong (Princeton University)\n\nTitle:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla\, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder\, the reproducibility and intrinsic nature of the oscillations\, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al.\, Nature Physics 17\, 915 (2021).Collaborators: Czajka\, Gao\, Hirschberger\, Lampen Kelley\, Banerjee\, Yan\, Mandrus and Nagler.\n\n\n\n\nDate TBA |10:30am ET\n\n\n\n\n\n\n\nSuchitra Sebastian (University of Cambridge) \nTitle: TBA\n\n\n\n\nDate TBA |10:30am ET\n\n\n\n\n\n\n\nJenny Hoffman (Harvard University) \nTitle: TBA
URL:https://cmsa.fas.harvard.edu/event/strongly-correlated-quantum-materials-and-high-temperature-superconductors-series/
CATEGORIES:Event,Strongly Correlated Quantum Materials and High-Temperature Superconductors
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DTSTART;TZID=America/New_York:20210331T103000
DTEND;TZID=America/New_York:20210331T120000
DTSTAMP:20260417T204626
CREATED:20240126T080956Z
LAST-MODIFIED:20240126T080956Z
UID:10001405-1617186600-1617192000@cmsa.fas.harvard.edu
SUMMARY:3/31/2021 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-31-2021-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210331T140000
DTEND;TZID=America/New_York:20210331T150000
DTSTAMP:20260417T204626
CREATED:20240126T075915Z
LAST-MODIFIED:20240126T191807Z
UID:10001399-1617199200-1617202800@cmsa.fas.harvard.edu
SUMMARY:3/31/2021 Random Matrix and Probability Theory Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-31-2021-random-matrix-and-probability-theory-seminar/
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210331T140000
DTEND;TZID=America/New_York:20210331T150000
DTSTAMP:20260417T204626
CREATED:20240212T073957Z
LAST-MODIFIED:20240212T073957Z
UID:10001877-1617199200-1617202800@cmsa.fas.harvard.edu
SUMMARY:Random Matrix & Probability Theory Seminar
DESCRIPTION:Beginning immediately\, until at least December 31\, all seminars will take place virtually\, through Zoom.\nIn the 2020-2021 AY\, the Random Matrix and Probability Theory Seminar will take place on select Wednesdays from 2:00 – 3:00pm virtually. This seminar is organized by Christian Brennecke (brennecke@math.harvard.edu ). \nTo learn how to attend this seminar\, please fill out this form. \nThe schedule below will be updated as the details are confirmed. \nSpring 2021:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n3/31/2021\nPhilippe Sosoe\, Cornell University\nTitle:  Fluctuation bounds for O’Connell-Yor type systems \nAbstract: The O’Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about this model thanks to remarkable algebraic structure uncovered by O’Connell\, Yor and others\, basic estimates for the behavior of the tails of the centered partition function for finite N that are available for zero temperature models are missing. I will present an iterative estimate to obtain strong concentration and localization bounds  for the O’Connell-Yor polymer on an almost optimal scale N^{1/3+\epsilon}. \nIn the second part of the talk\, I will introduce a system of interacting diffusions describing the successive increments of partition functions of different sizes. For this system\, the N^{2/3} variance upper bound known for the OY polymer can be proved for a general class of interactions which are not expected to correspond to integrable models. \nJoint work with Christian Noack and Benjamin Landon.\n\n\n4/7/2021\nYue M. Lu\, Harvard\nTitle: Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Random Matrices\n\nAbstract: In many problems in statistical learning\, random matrix theory\, and statistical physics\, one needs to simulate dynamics on random matrix ensembles. A classical example is to use iterative methods to compute the extremal eigenvalues/eigenvectors of a (spiked) random matrix. Other examples include approximate message passing on dense random graphs\, and gradient descent algorithms for solving learning and estimation problems with random initialization. We will show that all such dynamics can be simulated by an efficient matrix-free scheme\, if the random matrix is drawn from an ensemble with translation-invariant properties. Examples of such ensembles include the i.i.d. Gaussian (i.e. the rectangular Ginibre) ensemble\, the Haar-distributed random orthogonal ensemble\, the Gaussian orthogonal ensemble\, and their complex-valued counterparts.A “direct” approach to the simulation\, where one first generates a dense n × n matrix from the ensemble\, requires at least O(n^2) resource in space and time. The new algorithm\, named Householder Dice (HD)\, overcomes this O(n^2) bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance\, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles\, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are O(nT) and O(n T^2)\, respectively\, with T being the number of iterations. When T ≪ n\, which is nearly always the case in practice\, the new algorithm leads to significant reductions in runtime and memory footprint.Finally\, the HD algorithm is not just a computational trick. I will show how its construction can serve as a simple proof technique for several problems in high-dimensional estimation\n\n\n4/14/2021\nCanceled\n\n\n\n4/16/2021\nFriday\nPatrick Lopatto (IAS)\nTitle: Fluctuations in local quantum unique ergodicity for generalized Wigner matrices \nAbstract: In a disordered quantum system\, delocalization can be understood in many ways. One of these is quantum unique ergodicity\, which was proven in the random matrix context by Bourgade and Yau. It states that for a given eigenvector and set of coordinates J\, the mass placed on J by the eigenvector tends to N^{-1}|J|\, the mass placed on those coordinates by the uniform distribution. Notably\, this convergence holds for any size of J\, showing that the eigenvectors distribute evenly on all scales. \nI will present a result which establishes that the fluctuations of these averages are Gaussian on scales where |J| is asymptotically less than N\, for generalized Wigner matrices with smooth entries. The proof uses new eigenvector observables\, which are analyzed dynamically using the eigenvector moment flow and the maximum principle. \nThis is joint work with Lucas Benigni.\n\n\n4/21/2021\nJean-Christophe Mourrat\, Courant Institute\, NYU\nTitle: Mean-field spin glasses: beyond Parisi’s formula?\n\nAbstract: Spin glasses are models of statistical mechanics encoding disordered interactions between many simple units. One of the fundamental quantities of interest is the free energy of the model\, in the limit when the number of units tends to infinity. For a restricted class of models\, this limit was predicted by Parisi\, and later rigorously proved by Guerra and Talagrand. I will first show how to rephrase this result using an infinite-dimensional Hamilton-Jacobi equation. I will then present partial results suggesting that this new point of view may allow to understand limit free energies for a larger class of models\, focusing in particular on the case in which the units are organized over two layers\, and only interact across layers.\n\n\n\n\n\nFall 2020:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n9/9/2020\nYukun He (Zurich)\nTitle: Single eigenvalue fluctuations of sparse Erdős–Rényi graphs \nAbstract: I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdös-Rényi graph $G(N\,p)$. I show that if $N^{-1}\ll p \ll N^{-2/3}\, then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable\, which has the interpretation of the total degree of the graph. The main technical tool of the proof is a rigidity bound of accuracy $N^{-1-\varepsilon}p^{-1/2}$ for the extreme eigenvalues\, which avoids the $(Np)^{-1}$-expansions from previous works. Joint work with Antti Knowles.\n\n\n10/14/2020\nDavid Belius (University of Basel)\nTitle: The TAP approach to mean field spin glasses \nAbstract: The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated methods  in theoretical physics and mathematics\, such as the replica method\, which are largely orthogonal to the TAP approach. The TAP approach has the advantage of being interpretable as a variational principle optimizing an energy/entropy trade-off\, as commonly encountered in statistical physics and large deviations theory\, and potentially allowing for a more direct characterization of the Gibbs measure and its “pure states”. In this talk I will recall the TAP approach\, and present preliminary steps towards a solution of mean field spin glass models entirely within a TAP framework.\n\n\n10/28/2020\nGiuseppe Genovese (University of Basel)\nTitle: Non-convex variational principles for the RS free energy of restricted Boltzmann machines \nAbstract: From the viewpoint of spin glass theory\, restricted Boltzmann machines represent a veritable challenge\, as to the lack of convexity prevents us to use Guerra’s bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will present old and new results around the topic along with some open problems.\n\n\n11/4/2020\nBenjamin Landon (MIT)\nTitle:  Fluctuations of the spherical Sherrington-Kirkpatrick model \nAbstract:  The SSK model was introduced by Kosterlitz\, Thouless and Jones as a simplification of the usual SK model with Ising spins. Fluctuations of its observables may be related to quantities from random matrix theory using integral representations.  In this informal talk we discuss some results on fluctuations of this model at critical temperature and with a magnetic field\n\n\n11/11/2020\n3:00 – 4:00pm\nLucas Benigni (University of Chicago)\nTitle:  Optimal delocalization for generalized Wigner matrices \nAbstract: We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables\, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular\, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result\, known as delocalization\, to more general entry distributions. After giving a brief overview of the previous results going in this direction\, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau\, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.\n\n\n11/18/2020\nSimone Warzel (Technical University of Munich)\nTitle:  Hierarchical quantum spin glasses\n\nAbstract: Hierarchical spin glasses such as the generalised random energy model are known to faithfully model typical energy landscapes in the classical theory of mean-field spin glasses. Their built-in hierarchical structure is known to emerge spontaneously in the spin-glass phase of\, e.g.\, the Sherrington-Kirkpatrick model. In this talk\, I will review recent results on the effects of a transversal magnetic field on such hierarchical quantum spin glasses.\nIn particular\, I will present a formula of Parisi-type for their free energy which allows to make predictions about the phase diagram.\n\n\n12/2/2020\nSabine Jansen (LMU Munich)\nTitle: Thermodynamics of a hierarchical mixture of cubes\n\nAbstract: The talk discusses a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes of side-lengths 2^j\, j\in \N_0. Cubes belong to an admissible set such that if two cubes overlap\, then one cube is contained in the other\, a picture reminiscent of Mandelbrot’s fractal percolation model. I will present exact formulas for the entropy and pressure\, discuss phase transitions from a fluid phase with small cubes towards a condensed phase with a macroscopic cube\, and briefly sketch some broader questions on renormalization and cluster expansions that motivate the model. Based on arXiv:1909.09546 (J. Stat. Phys. 179 (2020)\, 309-340).\n\n\n\n\nFor information on previous seminars\, click here \nThe schedule will be updated as details are confirmed.
URL:https://cmsa.fas.harvard.edu/event/random-matrix-probability-theory-seminar/
CATEGORIES:Random Matrix & Probability Theory Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210331T150000
DTEND;TZID=America/New_York:20210331T160000
DTSTAMP:20260417T204626
CREATED:20240126T083143Z
LAST-MODIFIED:20240515T195507Z
UID:10001412-1617202800-1617206400@cmsa.fas.harvard.edu
SUMMARY:Doing Mathematics with Simple Types: Infinitary Combinatorics in Isabelle/HOL
DESCRIPTION:Speaker: Lawrence Paulson\, University of Cambridge Computer Laboratory  \nTitle: Doing Mathematics with Simple Types: Infinitary Combinatorics in Isabelle/HOL  \nAbstract: Are proof assistants relevant to mathematics? One approach to this question is to explore the breadth of mathematical topics that can be formalised. The partition calculus was introduced by Erdös and R. Rado in 1956 as the study of “analogues and extensions of Ramsey’s theorem”. Highly technical results were obtained by Erdös-Milner\, Specker and Larson (among many others) for the particular case of ordinal partition relations\, which is concerned with countable ordinals and order types. Much of this material was formalised last year (with the assistance of Džamonja and Koutsoukou-Argyraki). Some highlights of this work will be presented along with general observations about the formalisation of mathematics\, including ZFC\, in simple type theory. \n\n\n\n\n\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/3-31-2021-new-tech-in-math/
CATEGORIES:New Technologies in Mathematics Seminar
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