Simons Collaboration on Ultra-Quantum Matter Annual Meeting 2022

The third annual meeting of the Simons Collaboration on Ultra-Quantum Matter (UQM) was held in hybrid format January 20–21, 2022, with 39 in-person and 90 virtual participants.

The meeting began with an in-person talk by UQM PI Subir Sachdev on a new approach to the cuprate pseudogap problem. The non-perturbative aspects of the problem, especially Luttinger’s theorem and its violation in certain heavy-fermion models were highlighted, and a strategy to incorporate similar physics in the single-band model for cuprates along with a comparison between experiment and theory was presented.

UQM PI Victor Gurarie discussed work on new probes of quantum many-body systems via real-time quantum dynamics, some in collaboration with UQM PI Victor Galitski. The talk focused on the Loschmidt echo and its connection to spectral form factors and the partition function of statistical mechanics systems at imaginary temperature.

Some two-dimensional topological phases, such as fractional quantum Hall liquids, possess chiral edge states, characterized by a non-zero chiral central charge. While it is expected that all the information about a gapped phase should be encoded in its ground state wave function, it has long been unclear how to determine the chiral central charge directly from a bulk ground state. In a short talk, Bowen Shi discussed a new approach to this problem, employing a quantity known as the modular commutator. In a related talk, Mike Zaletel discussed characterization of tripartite entanglement, and in particular, the Markov gap, which is an entanglement diagnostic for the presence of ungappable edge states including — but not limited to — those with non-zero chiral central charge.

Jonathan Simon described the amazing progress his and other groups have made in creating and probing quantum matter in synthetic ultra-cold atom and optical systems. In a short talk, UQM Postdoc Ruben Verresen discussed realizations of long-range entangled states, i.e., ultra-quantum matter, by applying local measurements to ground states of symmetry-protected topological phases. Some of these schemes can be implemented in arrays of Rydberg atoms using existing experimental capabilities.

A second experimental talk of the meeting was delivered by Jie Shan which focused on the remarkable progress in studying magnetism and strongly correlated phenomena in moiré structures of transition metal dichalcogenides. A short theoretical talk was given by UQM Postdoc Zhu-Xi Luo who described a novel effective field theory approach to studying magnetism in moiré magnets.

Two talks reported on recent progress in classifying topological phases of matter. Christina Knapp discussed a proposed complete characterization and classification of fermionic topological phases with symmetry in two spatial dimensions, using the framework of G-crossed braided tensor categories previously developed for bosonic phases. In a short talk, UQM Postdoc Xueda Wen discussed work together with UQM PIs Michael Hermele and Ashvin Vishwanath on the classification and properties of parametrized quantum systems that generalize the Thouless charge pump in one spatial dimension. Here, new phenomena arise — for instance at spatial boundaries — upon considering a family of systems depending continuously on some external control parameters.

The meeting concluded with an in-person talk from Yi-Zhuang You, discussing novel applications of deconfined criticality to high-energy physics. This work at the interface between condensed matter and high-energy physics aims to situate the standard model within a phase diagram where other vacua are those of grand-unified theories. A number of intriguing deconfined critical points within this phase diagram were discussed.

The meeting was characterized throughout by a high level of engagement, with many questions and much discussion over Zoom, and of course also among in-person participants. A Zoom discussion room was utilized by virtual speakers to continue discussions after their talk with other virtual participants.

* = Remote talk

Victor Gurarie
University of Colorado Boulder

Spectral Form Factors and Evolution Operators of Quantum Systems
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Christina Knapp
California Institute of Technology & Microsoft Research

Characterization and Classification of Fermionic Symmetry Enriched Topological Phases
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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
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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
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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
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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
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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
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Mike Zaletel
University of California, Berkeley

Multi-partite entanglement in topological phases
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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.