Simons Collaboration on Ultra-Quantum Matter Annual Meeting 2022

Date & Time

Michael Hermele, University of Colorado, Boulder
Ashvin Vishwanath, Harvard University

Meeting Goals:
The two overarching goals of the Simons Collaboration on Ultra Quantum Matter (UQM) are to develop the theory of highly entangled quantum matter and to work towards physical realization, particularly in synthetic matter systems. The 2022 annual meeting will include a mix of condensed matter, high-energy, quantum information and atomic physicists. The meeting will cover recent progress in classifying and characterizing topological and fracton matter and in strongly coupled non-Fermi liquid phases. In addition, we will review recent rapid progress in synthetic matter platforms and discuss how to steer these developments toward more robust realizations of highly entangled states. Mirroring the convergence of different communities in recent exciting developments, the meeting will bring together a wide spectrum of theoretical physicists cutting across traditional boundaries, aiming to plant the seeds for further progress.

  • Agendaplus--large

    Thursday, January 20

    9:30 AMSubir Sachdev | Paramagnon Fractionalization Theory of the Pseudogap Metal of the Cuprates
    11:00 AMVictor Gurarie | Spectral Form Factors and Evolution Operators of Quantum Systems
    1:00 PMUQM Postdocs Lightning Talks

    Ruben Verresen* | Non-Abelian Topological Order and Fractons from Measuring Spts: From Theory to Practice
    Bowen Shi* | Chiral Central Charge from a Single Bulk Wave Function
    Zhu-Xi Luo* | Twisted Bilayer Dirac Spin Liquid
    Xueda Wen* | Flow of (Higher) Berry Curvature and Bulk-Boundary Correspondence in Parametrized Quantum Systems
    2:30 PMJonathan Simon* | Making Quantum Matter from Light: Laughlin Puddles, Mott Insulators, and Strongly Interacting Fluids
    4:00 PMChristina Knapp* | Characterization and Classification of Fermionic Symmetry Enriched Topological Phases

    Friday, January 21

    9:30 AMJie Shan* | 2D Moiré Quantum Materials
    11:00 AMMike Zaletel* | Multi-partite entanglement in topological phases
    1:00 PMYi-Zhuang You | Deconfined Quantum Criticality between Grand Unified Theories

    * = Remote talk

  • Abstracts & Slidesplus--large

    Victor Gurarie
    University of Colorado Boulder

    Spectral Form Factors and Evolution Operators of Quantum Systems
    View Slides (PDF)

    Christina Knapp
    California Institute of Technology & Microsoft Research

    Characterization and Classification of Fermionic Symmetry Enriched Topological Phases
    View Slides (PDF)

    Topological orders can be divided into two classes corresponding to whether the microscopic degrees of freedom supporting the phase are purely bosonic (e.g., spins or qubits) or whether they include fermions (e.g., electrons). Despite the ubiquity of fermionic phases in condensed matter systems and the intense interest in understanding the interplay of symmetry and topology, a general characterization and classification of fermionic topological order has remained elusive. In this talk, Knapp will discuss the results in arXiv:2109.10911 in which we use G-crossed braided tensor category theory to fully characterize and classify 2+1 dimensional fermionic symmetry enriched topological phases with onsite unitary fermionic symmetry group. She will review the tiered G-crossed classification of bosonic SET phases before diving into the richer structure of fermionic SET phases.

    Zhu-Xi Luo
    Kavli Institute for Theoretical Physics

    Twisted Bilayer Dirac Spin Liquid
    View Slides (PDF)

    When two layers of two-dimensional materials are assembled with a relative twist, moiré patterns can arise, giving rise to a tremendous wealth of exotic phenomena. In this work, we consider twisting two triangular lattices hosting Dirac quantum spin liquids. The single-layer parent state is stable, since the proliferation of monopole operators, inducing conventional long-range magnetic or valence bond solid order, is symmetry forbidden. Conversely in the bilayer system, interlayer monopole tunneling is a symmetry-allowed relevant perturbation and can lead to ordered bilayer states. Adding a relative twist between the two layers reduces the stability of the ordered phases compared with the untwisted case and results in tunable moiré modulations of antiferromagnetic and valence bond solid order parameters. This is work done in collaboration with Urban F. P. Seifert and Leon Balents.

    Subir Sachdev
    Harvard University

    Paramagnon Fractionalization Theory of the Pseudogap Metal of the Cuprates
    View Slides (PDF)

    Jie Shan
    Cornell University

    2-D Moiré Quantum Materials

    When two van der Waals materials of slightly different orientation or lattice constant are overlaid, a moiré pattern emerges. The moiré pattern introduces a new length scale, many times the lattice constant of the original materials, for Bragg scattering of Bloch electrons in each layer. This gives rise to flat moiré minibands and rich emergent quantum phenomena. In this talk, Shan will review recent progress on the development of 2-D semiconductor moiré materials and realization of different many-body Hamiltonians. Shan will also discuss the opportunities and challenges in designing moiré materials and developing quantum simulators based on these artificial materials.

    Bowen Shi
    University of California, San Diego

    Chiral Central Charge from a Single Bulk Wave Function
    View Slides (PDF)

    A (2+1)-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current, at low temperatures, is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. Shi derives a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. He will numerically test our prediction for a bosonic lattice Laughlin state. The result of extrapolation is consistent with the proposed formula up to an error of about 0.7 percent.

    Ruben Verresen
    Harvard University

    Non-Abelian Topological Order and Fractons from Measuring Spts: From Theory to Practice

    A defining property of topological order is that it is difficult to create by any unitary process, requiring a time proportional to system size. Here Verresen will discuss a loophole which obtains these states from single-site measurements on symmetry-protected topological (SPT) phases. This generalizes previously known examples, such as measuring the cluster state to obtain the toric code, by observing that one can physically enact the Kramers–Wannier or Jordan–Wigner transformation on an arbitrary initial state. Remarkably, some of these schemes can be implemented in existing Rydberg atom array platforms to efficiently create non-abelian topological order and potentially the first experimental realization of fracton order.

    Based on work with Nat Tantivasadakarn, Ryan Thorngren and Ashvin Vishwanath.

    Xueda Wen
    Massachusetts Institute of Technology
    View Slides (PDF)

    Flow of (Higher) Berry Curvature and Bulk-Boundary Correspondence in Parametrized Quantum Systems

    In this talk, Wen will discuss the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian, one considers a family of Hamiltonians that depend continuously on some parameters. In particular, Wen will formulate a bulk-boundary correspondence for an important bulk quantity, the Kapustin–Spodyneiko higher Berry curvature, first in one spatial dimension and then in arbitrary dimension. The bulk-boundary correspondence gives the d-dimensional higher Berry curvature an interpretation as a flow of (d-1)-dimensional higher Berry curvature to/from spatial boundaries. Wen will also present a pair of general quantum pumping constructions based on physical pictures introduced by Kitaev, which take as input a d-dimensional parametrized system, and produce new (d+1)-dimensional parametrized systems. These constructions are useful for generating examples, and Wen conjectures that one of the constructions realizes the suspension isomorphism in a generalized cohomology theory of invertible phases.

    Yi-Zhuang You
    University of California, San Diego

    Deconfined Quantum Criticality between Grand Unified Theories
    View Slides (PDF)

    Mike Zaletel
    University of California, Berkeley

    Multi-partite entanglement in topological phases
    View Slides (PDF)

    The strong-coupling approach to magic-angle bi- and tri-layer graphene has many beautiful implications, including an emergent, enlarged symmetry group and the potential for ‘skyrmion superconductivity.’ However, strain, which appears to be ubiquitous in most samples, modifies the band structure in a manner which pushes the system toward intermediate coupling. Finally, Zaletel will present theoretical and DMRG evidence that strain may be a necessary ingredient for understanding the phase diagram of these systems.


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