CMSA

Dipolar and modulated symmetry protected topological phases
2023-10-04 10:30 - 11:30 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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.

Breaking ergodicity: quantum scars and regular eigenstates
2023-10-16 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411, in peer review.

Composite fermions and the fractional quantum anomalous Hall effect
2023-10-18 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs), I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.

Unveiling Correlated Topological Insulators through Fermionic Tensor Network States
2023-11-01 10:30 - 11:30 | 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 equations, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems.

Landscape of quantum phases in quantum materials
2023-11-02 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.

Uniqueness of Landau levels and their analogs with higher Chern numbers
2023-11-09 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 levels and their analogs with higher Chern numbers. arXiv:2304.00866, 2023. arXiv:2304.00866.

A bulk gap in the presence of edge states for a truncated Haldane pseudopotential
2023-11-15 10:30 - 11:30 | 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 to the presence of edge modes; in contrast, for periodic boundary conditions, the gap remains robustly order one in the same radius limit. The standard scheme for applying spectral gap estimating techniques to the model with periodic boundary conditions, though, produces a lower bound on the bulk gap that still reflects the energy of the edge modes. To obtain an estimate on the bulk gap that reflects its true behavior, a new gap estimating strategy was developed. By customizing the spectral gap method to key invariant subspaces of the Hamiltonian, we are able to successfully avoid the edge states and produce a more accurate lower bound on the bulk gap. In this talk, we discuss this invariant subspace strategy for proving bulk gaps in the presence of edge states. This is based off joint work with S. Warzel.

Emergent composite-fermion Luttinger liquid at the half-filled Landau level
2023-11-20 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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.

Anomalous Landau level analog in solids: search and implications for 2d heterostructures
2023-11-29 17:00 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 of graphene. In particular, I will derive the generic form of Bloch wave functions realizing the analog of such anomalous Landau levels, and argue that twisted transition metal dichalcogenides homobilayers (in which fractional Chern insulators were first discovered) almost realize such anomalous bands.

Quantum information: the interplay of mathematics and physics
2023-12-01 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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).

The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future
2023-12-04 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 5/2 state, but its underlying nature is still under debate.
In this talk, I will review the basics of the 5/2 state [1] and a more unified theoretical description of different possible topological orders of the 5/2 state that we have recently proposed [2]. I will also review the groundbreaking thermal Hall conductance experiment [3] and the follow-up quantum Hall interface experiments by the Weizmann Institute group [4, 5], and discuss what possible lessons that we can learn from the experimental results. Lastly, I will talk about some possible directions and related topics for future investigations.
References:
[1] K. K. W. Ma, M. R. Peterson, V. W. Scarola, and K. Yang, “Fractional quantum Hall effect at the filling factor ν = 5/2” in Encyclopedia of Condensed Matter Physics (Second Edition), edited by T. Chakraborty, Academic Press (2024).
[2] K. K. W. Ma and D. E. Feldman, “The sixteenfold way and the quantum Hall effect at half-integer filling factors”, Phys. Rev. B 100, 035302 (2019).
[3] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern, “Observation of half-integer thermal Hall conductance”, Nature (London) 559, 205 (2018).
[4] B. Dutta, W. Yang, R. Melcer, H. K. Kundu, M. Heiblum, V. Umansky, Y. Oreg, A. Stern, D. Mross, “Distinguishing between non-Abelian topological orders in a quantum Hall system”, Science 375, 193 (2021).
[5] B. Dutta, V. Umansky, M. Banerjee, and M. Heiblum, “Isolated ballistic non-Abelian interface channel”, Science 377, 1198 (2022).
