During the Fall 2023 semester, the CMSA will host a seminar on Topological Quantum Matter organized by Jie Wang. (The seminar will not run in Spring 2024). This seminar takes place on Wednesdays from 10:30–11:30 am (Eastern time). The meetings are held in Room G10 at the CMSA, 20 Garden Street, Cambridge MA 02138, and some meetings will take place virtually on Zoom or be held in hybrid formats. To learn how to attend, please fill out this form.

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  • December 04, 2023 02:00 PM
Speaker: Ken K. W. Ma
Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker:  Ken K. W. Ma (Northeastern University) Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future Abstract: The discovery of fractional quantum Hall (FQH) states started a new chapter in modern physics. Nowadays, more than 70 FQH states at different filling factors have been observed. Among them, the FQH state at the filling factor ν=5/2 in GaAs (or the 5/2 state) remains one of the most special and attractive states. Since its discovery in 1987, different possible topological orders have been proposed to describe the 5/2 state. Some of them can host an exotic type of particles, known as non-Abelian anyons. Recent experiments have provided more insights into the understanding of the…

  • December 01, 2023 04:30 PM
Speaker: Kaifeng Bu
Title: Quantum information: the interplay of mathematics and physics
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Kaifeng Bu (Harvard University) Title: Quantum information: the interplay of mathematics and physics Abstract: I will provide an introduction to quantum information, which points to a new connection with experiment on the one hand, and a potential new area of mathematical analysis on the other. I will introduce two recent results about the application of this new area in quantum information: (1) a novel Quantum Central Limit Theorem (QCLT), and (2) a physically realizable protocol for testing and measuring quantum advantage. This talk is based on a collaboration with Arthur Jaffe, and Weichen Gu (PNAS120(25)2023, arXiv: 2302.08423, arXiv:2306.09292).  

  • November 29, 2023 05:00 PM
Speaker: Valentin Crepel
Title: Anomalous Landau level analog in solids: search and implications for 2d heterostructures
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Valentin Crepel, Flatiron Institute Title: Anomalous Landau level analog in solids: search and implications for 2d heterostructures Abstract: The recent experimental observation of fractional Chen insulators — the analog of fractional quantum Hall states realized in absence of any applied magnetic field — calls for more detailed theoretical investigations of the special conditions allowing their emergence. To gain some insight on this problem, we can rely on (i) our extensive knowledge of the physical properties of Landau levels, and (ii) the identification of their exact solid state analogs. In this talk, (i-ii) will be discussed in the case of ”anomalous Landau levels”, which are protected by an index theorem, and whose most famous representative are the zero-th Landau levels…

  • November 20, 2023 02:00 PM
Speaker: Prashant Kumar
Title: Emergent composite-fermion Luttinger liquid at the half-filled Landau level
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Prashant Kumar, University of Chicago Title: Emergent composite-fermion Luttinger liquid at the half-filled Landau level Abstract: The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, I will present our numerical calculations of the excitation spectrum of this state on infinite cylinders. By comparing our results with a quasi-1D theory of CFs, we show compelling quantitative evidence for the emergence of a Luttinger liquid of composite-fermions at low energies, distinct from that of electrons. I will comment on some future directions.

  • November 15, 2023 10:30 AM
Speaker: Amanda Young
Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential
Venue: virtual

Topological Quantum Matter Seminar Speaker: Amanda Young, UIUC Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential Abstract: Haldane pseudopotentials were first introduced as Hamiltonian models for the fractional quantum Hall effect, and it has been long expected that they should exhibit the characteristic properties of this exotic phase of matter, including a spectral gap above the ground state energy. We will discuss recent work that verified this gap conjecture for a truncated version of the 1/3-filled Haldane pseudopotential in the cylinder geometry. Numerical evidence suggested that for open boundary conditions the gap of the truncated model closes as the cylinder radius converges to zero and that this closure is due…

  • November 09, 2023 04:30 PM
Speaker: Bruno Mera
Title: Uniqueness of Landau levels and their analogs with higher Chern numbers
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Bruno Mera, Instituto Superior Tecnico Title: Uniqueness of Landau levels and their analogs with higher Chern numbers Abstract: Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged par- ticle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this talk, using the Stone-von Neumann the- orem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions. Ref: Bruno Mera and Tomoki Ozawa. Uniqueness of Landau…

  • November 02, 2023 04:30 PM
Speaker: Liujun Zou
Title: Landscape of quantum phases in quantum materials
Venue: CMSA Room G10

Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar Speaker: Liujun Zou (Perimeter Institute) Title: Landscape of quantum phases in quantum materials Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various…

  • November 01, 2023 10:30 AM
Speaker: Shenghan Jiang
Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States
Venue: virtual

Topological Quantum Matter Seminar Speaker: Shenghan Jiang, Kavli Institute for Theoretical Sciences UCAS Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States Abstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has been established that topological insulator phases persist as stable phases. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wavefunctions for numerical simulations is highly desirable. In this talk, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions, we write down tensor…

  • October 18, 2023 12:30 PM
Speaker: Hart Goldman
Title: Composite fermions and the fractional quantum anomalous Hall effect
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Hart Goldman, University of Chicago Title: Composite fermions and the fractional quantum anomalous Hall effect Abstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk, I will argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new zero-field context. In particular, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end, I will present exact diagonalization evidence for such composite Fermi liquid states at…

  • October 16, 2023 02:00 PM
Speaker: Ceren Dag
Title: Breaking ergodicity: quantum scars and regular eigenstates
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Ceren Dag, Harvard Title: Breaking ergodicity: quantum scars and regular eigenstates Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics, spectrum, and phase space, consisting of…

  • October 10, 2023 04:00 PM
Speaker: Daniele Guerci
Title: Chern Mosaic and ideal bands in helical trilayer graphene
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Daniele Guerci, Flatiron Institute Title: Chern Mosaic and ideal bands in helical trilayer graphene Abstract: In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat bands features the…

  • October 04, 2023 10:30 AM
Speaker: Ho Tat Lam
Title: Dipolar and modulated symmetry protected topological phases
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Ho Tat Lam, MIT Title: Dipolar and modulated symmetry protected topological phases Abstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.

  • September 20, 2023 10:30 AM
Speaker: Jonah Herzog-Arbeitman
Title: Exact Results in Flat Band Hubbard Models
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Jonah Herzog-Arbeitman, Princeton University Title: Exact Results in Flat Band Hubbard Models Abstract: Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multi-orbital case: the mean-field theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and low-energy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution…

  • September 13, 2023 10:30 AM
Speaker: Xueyang Song
Title: Phase transitions out of quantum Hall states in moire TMD bilayers
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Xueyang Song (MIT) Title: Phase transitions out of quantum Hall states in moire TMD bilayers Abstract: Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\’e Transition Metal Dichalcogenide (TMD) bilayers, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth.  At filling -2/3, we describe a direct transition between the FQAH state and a Charge Density Wave (CDW) insulator. The critical theory resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi…

  • September 12, 2023 04:00 PM
Speaker: Roman Geiko
Title: Homotopy classes of loops of Clifford unitaries
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Roman Geiko, UCLA Title: Homotopy classes of loops of Clifford unitaries Abstract: We study Clifford locality-preserving unitaries and stabilizer Hamiltonians by means of Hermitian K-theory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two short-range entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu.  https://arxiv.org/abs/2306.09903.

  • December 07, 2022 10:00 AM
Speaker: Vasil Rokaj
Title: Controlling Quantum Matter with Quantum Cavity Fields
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Vasil Rokaj (Harvard) Title: Controlling Quantum Matter with Quantum Cavity Fields Abstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free…

  • November 23, 2022 09:00 AM
Speaker: Jian Kang
Title: Continuum field theory of graphene bilayer system
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Jian Kang, School of Physical Science and Technology, ShanghaiTech University, Shanghai, China Title: Continuum field theory of graphene bilayer system Abstract: The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the magic-angle twisted bilayer graphene (MATBG), and nowadays is a starting point for most theoretical works. In this talk, I will briefly review the BM model and then present a continuum field theory [1] for graphene bilayer system allowing any smooth lattice deformation including the small twist angle. With the gradient expansion to the second order, the continuum theory for MATBG [2] produces the spectrum that almost perfectly matches the spectrum of the microscopic model, suggesting the validity of…

  • November 16, 2022 10:00 AM
Speaker: Jérôme Faist
Title: Vacuum fluctuations in cavities: breakdown of the topological protection in the integer Quantum Hall effect
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Jérôme Faist  (ETH Zurich) Title: Vacuum fluctuations in cavities: breakdown of the topological protection in the integer Quantum Hall effect Abstract: When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling ΩR is such that the coupling energy becomes close to the one of the bare matter resonance ω0. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian. In a microcavity, the strength of…

  • November 02, 2022 09:00 AM
Speaker: Junyeong Ahn
Title: Optical axion electrodynamics
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Junyeong Ahn (Harvard) Title: Optical axion electrodynamics Abstract: Electromagnetic fields in a magneto-electric medium behave in close analogy to photons coupled to the hypothetical elementary particle, the axion. This emergent axion electrodynamics is expected to provide novel ways to detect and control material properties with electromagnetic fields. Despite having been studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Formulating axion electrodynamics at general optical frequencies requires resolving the difficulty of calculating optical magneto-electric coupling in periodic systems and demands a proper generalization of the axion field. In this talk, I will introduce a theory of optical axion electrodynamics that allows for a simple quantitative…

  • October 26, 2022 09:00 AM
Speaker: Bruno Mera
Title: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
Venue: CMSA Room G10

Topological Quantum Matter Seminar Speaker: Bruno Mera, Tohoku University Title: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry Abstract: The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of…