2023 Simons Collaboration on Ultra Quantum Matter Annual Meeting

The fourth annual meeting of the Simons Collaboration on Ultra-Quantum Matter (UQM) was held January 19–20, 2023, with over 90 in person participants. In addition to the speakers, UQM PIs and postdoctoral fellows, review panelists and many other students and postdocs, the meeting was attended by over ten other faculty members working on various aspects of UQM.

The meeting began with an overview of the UQM program by the Collaboration Director Ashvin Vishwanath. Highlights of research over the past three years — including classifications of gapped phases of matter, the anomaly approach to gapless compressible states, as well as realizations of ultra-quantum matter — were discussed alongside the significant efforts to build a community through a postdoc program, meetings and seminars.

This was followed by Shu Heng Shao (Stony Brook), a former UQM postdoctoral fellow, whose talk was appropriately named “Harmony of Symmetries” and focused on a series of models with unusual symmetries. A remarkable observation is that models with “harmonic” symmetry, a lattice limit of quantum Lifshitz models, have a very large ground state degeneracy on graphs with a coordination number that exceeds two, corresponding to a well known quantity in graph theory. Further, these kinds of degeneracies were shown to be present even away from fine-tuned models, and generically stabilized by couplings in a third dimension. Progress and challenges in field theory descriptions of fractons were also discussed.

In a separate talk on gapped topological phases, UQM PI John McGreevy (UCSD) gave a pedagogical introduction to the topological bootstrap program and its current status. This program is part of the question on how to characterize a state of UQM from its ground state wave function alone, which has implications for numerical simulations and experimental probes of UQM. McGreevy also discussed a recent promising approach pioneered by UCSD graduate student Ting-Chun (David) Lin on extending ideas from the entanglement bootstrap to 1+1D conformal field theories.

UQM PI Dam Son (Chicago) then turned to the best known example of a compressible phase, the Fermi liquid, but treated it within a fresh bosonization approach, “the method of coadjoint orbits.” This approach renders loop diagrams that require integration into tree level calculations. UQM PI Leon Balents (KITP) spoke about the transport theory of a different gapless system — phonons — and in particular how they could give rise to a thermal Hall effect in insulating magnets. Given the central role thermal Hall effect plays as a probe of spin liquid physics, understanding these effects quantitatively in other settings is of prime importance.

Ana Maria Rey (CU Boulder) discussed promising platforms for simulating quantum matter in cold atom systems, focusing in particular on current and near-term experiments in dipolar molecules. Prospects include the generation of entangled states via pair production and the realization of Berry phase phenomena analogous to bilayer graphene in two-dimensional dipolar molecule systems.

Monika Aidelsburger (Munich) gave an outstanding review of experimental techniques in quantum gas microscopes and new developments in her research group on simulating Floquet Hamiltonians and lattice gauge theories. Key developments include the observation of anomalous chiral edge modes in a Floquet system, and a planned experiment to generate dynamical gauge fields in a system of Yb atoms.

Mike Zaletel (Berkeley) talked about a new approach to numerical simulations of highly entangled quantum systems in D>1 being developed in his group, the isometric tensor networks, and showed promising preliminary results on simulating Chern insulators and their dynamics.

The meeting was marked by a highly interactive and stimulating atmosphere and the attendees were excited to be back to in person activities after the previous two remote/hybrid annual meetings. Several attendees stayed behind after the last talk brainstorming new directions and discussing recent developments.

Monika Aidelsburger
Fakultät für Physik, Ludwig-Maximilians-Universität München &
Munich Center for Quantum Science and Technology (MCQST)

Quantum Simulation with Ultracold Atoms – From Hubbard Models to Gauge Theories
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Well-controlled synthetic quantum systems, such as ultracold atoms in optical lattices, offer intriguing possibilities to study complex many-body problems in regimes that are beyond reach using state-of-the-art classical computations. The basic idea is to construct and use a well-controlled quantum many-body system in order to study its in- and out-of-equilibrium properties and potentially use it to develop more efficient tailored numerical methods that can then be applied to other systems that are not directly accessible with the simulator.

An important future quest concerns the development of novel experimental techniques that allow us to expand the range of models that can be accessed. Monika Aidelsburger will demonstrate this using the example of topological lattice models, which in general do not naturally appear in cold-atom experiments. Aidelsburger will show how the technique of periodic driving, also known as Floquet engineering, facilitates their realization and show how charge-neutral atoms in lattices can mimic the behavior of charged particles in the presence of an external magnetic field.

A key ingredient for quantum simulation is the degree of control one has over the individual particles and the microscopic parameters of the model. We have recently succeeded to not only use the technique of periodic driving to emulate physical systems that we know exist in nature, but to take this idea one step further and realize completely new topological regimes that do not have any static analog. Moreover, we are currently developing a novel hybrid optical lattice platform, where tightly focused optical tweezers are used to locally control the motion of the atoms in the lattice, paving the way towards quantum simulation of simplified lattice gauge theories, which play a fundamental role in a variety of research areas including high-energy physics and topological quantum computation.
 

Leon Balents
Kavli Institute for Theoretical Physics

Strong Correlation Physics of Mott and Wigner Crystals in Two-Dimensional Non-Graphene Moiré Systems
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Moiré patterns provide realizations of interacting electron physics on a lattice in two-dimensional transition metal dichalcogenide structures. Leon Balents will discuss prospects to observe strong correlation physics and ultra-quantum phases of matter in this framework and will focus on phenomena beyond local mean field theories like Hartree–Fock, which are the de facto standard.
 

John McGreevy
University of California, San Diego

Entanglement Bootstrap in Various Dimensions
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The Entanglement Bootstrap is a program to understand the universal properties of quantum matter starting from a representative density matrix on a ball. Much (perhaps all) of the structure of topological quantum field theory can be extracted starting from a state satisfying two axioms that implement the area law for entanglement. In this talk, based on work with Bowen Shi, Jin-Long Huang and Xiang Li, John McGreevy will describe how to use these methods to construct groundstates on a large class of manifolds. One important application of this construction is to demonstrate the property of remote detectability of topological excitations, an assumption of topological field theory. Another is to construct generalized symmetry algebras. These methods are also useful for understanding symmetry-enriched topological phases.
 

Ana Maria Rey
University of Colorado Boulder / NIST

Quantum Engineering of Pair Production Process in Spin Models in Multi-Layers: From Two-Mode Squeezing to Topological Kitaev Models
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Understanding and controlling the growth and propagation of quantum correlations and entanglement is an emerging frontier in non-equilibrium many-body physics, and a crucial key step for unlocking the full advantage of quantum systems. In this talk, Ana Maria Rey will discuss how in multi-layer spin systems, currently accessible in a broad range of quantum platforms, such as arrays of neutral atoms, Rydberg atoms, magnetic atoms and polar molecules, spin interactions can be utilized to realize in a controllable manner a variety of correlated pair-production processes. In particular, Rey will describe how in bi-layer systems, the capability to select individual layers and prepare targeted initial states, can enable the generation of iconic two-mode squeezing models that feature exponential growth of entanglement and are relevant in many contexts ranging from the foundations of quantum mechanics, to parametric amplification in quantum optics, to the Schwinger effect in high-energy physics and Unruh thermal radiation in general relativity. In multi-layers Rey will show it is possible to engineer a chiral bosonic Kitaev model featuring chiral propagation of correlations. Overall in this talk, Rey will report how current single-layer addressing capabilities can allow shaping and controlling the temporal growth and spatial propagation of quantum correlations in a variety of spin systems relevant for quantum simulation.
 

Shu-Heng Shao
Stony Brook University

Harmony of Symmetries

We will discuss lattice and continuum models ranging from those related to fractons, to compact Lifshitz theory, and to tensor gauge theory. These models have exotic global symmetries, which are the underlying reasons why they defy a standard continuum limit. We also discuss the anomalies of these global symmetries and their realizations on the lattice. Finally, we present a class of lattice models that can be defined on general graphs, which include a robust stabilizer code with lineon excitations.
 

Dam Thanh Son
University of Chicago

Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
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Dam Thanh Son and collaborators have developed a new method for bosonizing the Fermi surface based on the formalism of the coadjoint orbits. This allows one to parametrize the Fermi surface by a bosonic field that depends on the spacetime coordinates and on the position on the Fermi surface. The Wess–Zumino–Witten term in the effective action, governing the adiabatic phase acquired when the Fermi surface changes its shape, is given by the Kirillov–Kostant–Souriau symplectic form on the coadjoint orbit. Together with a Hamiltonian, the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Extensions of the theory that incorporate spin degrees of freedom and the BCS order parameter are discussed.
 

Ashvin Vishwanath
Harvard University

Ultra Quantum Matter
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The investigation of new states of matter made possible by long-range quantum entanglement represents a fundamental frontier of science that is seeing rapid progress. Ashvin Vishwanath will describe our collaboration’s efforts to classify such ultra quantum matter, to pinpoint their patterns of entanglement and physical properties and to realize and identify them in the laboratory. Promising future directions in the study of both gapped states, such as topological orders and fractons, as well as gapless states including novel metallic phases and the realization of such states particularly in synthetic quantum systems, will be outlined.
 

Mike Zaletel
University of California, Berkeley

Local Detection of Symmetry Breaking in Magic Angle Graphene

As the electron density is tuned through the flat bands of magic-angle graphene, numerous experiments indicate there is a “cascade” of symmetry-breaking transitions that reduce the degeneracy of the Fermi surface. Due to the combination of spin, valley and sub lattice degrees of freedom, there are many possible patterns of symmetry breaking, each with their own implications for superconductivity. Despite myriad theoretical predictions, to date there is no experimental detection of the order parameter. Mike Zaletel will present an analysis of recent local probe experiments which provide definitive detection of the order parameter of the \(\nu = \pm 2\) insulator and its behavior upon doping.