# Simons Collaboration on Ultra-Quantum Matter Annual Meeting 2020

• Organized by
• Ashvin Vishwanath, Ph.D.Harvard University
• Michael Hermele, Ph.D.University of Colorado Boulder
Date & Time

The first meeting of the Simons Collaboration on Ultra-Quantum Matter (UQM) was attended by UQM PIs, postdocs and students, as well as several other PIs and junior researchers in the field. Over a hundred participants attended the meeting.

QFT and Quantum Matter: The meeting began with a rousing talk by Shiraz Minwalla on developing quantum field theoretic methods to studying strongly interacting 2+1D systems. He described Chern-Simons theories with matter at large N and their dualities. He emphasized new ideas on viewing the dualities in terms of parton degrees of freedom and presented new results on these theories in a background magnetic field. These advances raised the exciting possibility of applying these theoretical tools to the study of fractional quantum Hall states. Shamit Kachru discussed surprising connections between AdS/CFT approaches to non-Fermi liquid metallic states and large-dimension limits of quantum systems, such as the Hubbard model, including via approaches such as dynamical mean field theory. In both cases, local criticality arises, associated with an emergent AdS2 geometry in the AdS/CFT case. Ashvin Vishwanath discussed field theoretical formulations of polarization and effective theories of quantum magnets with emergent gauge fields. These theories feature magnetic monopole excitations, and the quantum numbers of these magnetic monopoles play a key role in understanding their phase diagram. Vishwanath discussed a calculation of these magnetic monopole quantum numbers and the surprising connection to band topology. These calculations establish the stability of a certain type of ‘Dirac’ quantum spin liquid. Experiments on the triangular lattice that may have sighted this state were also reviewed.

Topological Phases: Michael Levin gave a crystal-clear talk on symmetry-protected topological phases and in particular how the defining features of such a phase could be extracted from the properties of domain wall excitations at the edge. This presentation attracted much interest and multiple follow-up questions from researchers in this field.

Synthetic Matter: Immanuel Bloch described the amazing progress his and other groups have made in creating and probing quantum matter in synthetic ultra-cold atom systems. It has become possible to cool atoms in optical lattices to temperatures significantly below magnetic-exchange energy scales. This goes along with remarkable advances in probing these systems, where atomic position and spin can now be imaged at the single-atom level, enabling the measurements of multipoint correlation functions and even nonlocal operators. These developments hold particular promise given that many ultra-quantum phases are characterized by nonlocal orders. In a similar vein, Peter Zoller presented theoretical results and theory-experiment collaborations, where ensembles of random unitary operators are used to measure nonlocal observables, such as entanglement entropy and invariants of topological phases. These ideas have been demonstrated in the context of programmable analog quantum simulators that, in the future, are expected to provide laboratory realizations of a range of ultra-quantum states.

Fractons: The meeting concluded with a pair of talks on fracton phases of matter: one from a condensed-matter viewpoint (Michael Hermele) and one from the viewpoint of continuum QFT (Nathan Seiberg). Both talks emphasized the challenges in connecting these exotic ultra-quantum phases to QFT and the crucial need to combine perspectives from multiple traditional subfields of theoretical phases. Hermele and Seiberg largely focused on exploring the nature and role of unusual symmetries present in fracton phases and their effective theories, both in lattice models and in the continuum. This surprising convergence of ideas from two different communities promises to drive research in fracton phases in exciting new directions over the next few years.

• Agenda

#### Thursday, January 23

 9:30 AM Shiraz Minwalla | Matter Chern Simons Theories: Lessons from Large N 11:00 AM Shamit Kachru | Black Holes at Large D and DMFT 1:00 PM Michael Levin | Computing Anomalies in SPT Edge Theories 2:30 PM Ashvin Vishwanath | Two Uses of Instantons in Solids: Probing Polarization and Characterizing Spin Liquids 4:00 PM Immanuel Bloch | Quantum Matter Under the Microscope

#### Friday, January 24

 9:30 AM Peter Zoller | Quantum Simulations with Atoms 11:00 AM Michael Hermele | Symmetries of Fracton Phases 1:00 PM Nathan Seiberg | Field Theories with Exotic Global Symmetries
• Public Lecture

Subir Sachdev, Harvard University
Ultra-Spooky Action at a Distance: From Quantum Materials in the Lab to Black Holes

• Abstracts

Shiraz Minwalla
Tata Institute of Fundamental Research

Matter Chern Simons Theories: Lessons from Large N

$$SU(N)_k$$ theories coupled to fundamental matter turn out to be exactly solvable in the large t’ Hooft large $$N$$ limit, $$N \to \infty$$, $$k \to \infty$$, $$N/k= \lambda$$= fixed. Over the last eight years, a great deal has been discovered about these models in this limit, including exact results for their phase diagrams, S matrices, thermal free energies, spectrum of operators and correlations functions. In this talk, Minwalla will review lessons learned from these studies and discuss open questions.

Shamit Kachru
Stanford University

Black Holes at Large D and DMFT

One can obtain non-Fermi liquids using holographic methods; a starring role is played by the emergent near-horizon AdS2 geometry of the charged black hole with higher dimensional AdS asymptotics. Here, Kachru studies these black holes and the resulting non-Fermi liquids in the limit of large dimension D and describe connections to the large D results, which come out of an a priori completely different line of development, DMFT.

Michael Levin
University of Chicago

Computing Anomalies in SPT Edge Theories

A general property of (2+1)-D symmetry-protected topological (SPT) phases is that their edges host gapless modes that are extremely robust. These edge modes provide a powerful tool for probing SPT phases, and in particular, it is believed that the low-energy theory of the edge uniquely determines the bulk SPT phase. In this talk, Levin will discuss a way to make this bulk-edge correspondence explicit; he will present a general method for identifying a (2+1)-D SPT phase from a (1+1)-D edge theory. In the language of quantum field theory, this method provides a systematic way to compute anomalies in (1+1)-D SPT edge theories with internal symmetries.

Ashvin Vishwanath
Harvard University

Two Uses of Instantons in Solids: Probing Polarization and Characterizing Spin Liquids

Polarization is a fundamental property of an insulating crystal. Vishwanath shows how test monopoles (instantons) lead to a nonperturbative definition, which can be used to calculate the polarization in strongly interacting systems. When the gauge fields are dynamical, as in theories describing quantum spin liquids, similar considerations allow us to fix the quantum numbers of monopoles. This talk will cover how this can help characterize Dirac spin liquids and possible realizations on the triangular lattice.

Immanuel Bloch
Max Planck Institute of Quantum Optics

Quantum Matter Under the Microscope

More than 30 years ago, Richard Feynman outlined his vision of a quantum simulator for carrying out complex calculations on physical problems. Today, his dream is a reality in laboratories around the world. This has become possible by using complex experimental setups of thousands of optical elements, which allow atoms to be cooled to Nanokelvin temperatures, where they almost come to rest. Recent experiments with quantum gas microscopes allow for an unprecedented view and control of such artificial quantum matter in new parameter regimes and with new probes. In our fermionic quantum gas microscope, we can detect both charge and spin degrees of freedom simultaneously, thereby gaining maximum information on the intricate interplay between the two in the paradigmatic Hubbard model. In his talk, Bloch will show how we can reveal hidden magnetic order, directly image individual magnetic polarons or probe the fractionalization of spin and charge in dynamical experiments. For the first time, we thereby have access to directly probe nonlocal ‘hidden’ correlation properties of quantum matter and to explore its real space resolved dynamical features also far from equilibrium. Bloch will also discuss our most recent experiments on realizing bilayer Fermi-Hubbard system with tunable couplings and how such a setting can be used to realize a novel 2-D spin and charge resolved detection for quantum gas microscopy experiments.

Peter Zoller
University of Innsbruck

Quantum Simulations with Atoms

Cold atoms and ions constitute not only a platform to build highly controlled quantum many-body systems, but also provide us with a unique toolbox to develop and implement novel measurement protocols for many-body observables. In this talk, Zoller will first discuss novel protocols based on randomized measurements, where statistical correlations between measurements probabilities allow us to access quantities from entanglement (Renyi) entropies to out-of-time ordered correlation function and topological invariants and provide us with protocols to perform cross-platform validation of quantum simulators. Furthermore, Zoller will discuss protocols allowing (quantum non-demolition) measurement of the many-body Hamiltonian (i.e., single-shot measurements of `the energy’ of a many-body system) and applications. Finally, he provides an outlook on how quantum simulators can be interfaced with small-scale quantum devices, providing quantum memory and a minimal set of quantum operations to analyze many-body quantum states and dynamics of quantum simulators.

Michael Hermele

Symmetries of Fracton Phases

Fracton phases are a new class of quantum phases of matter that are of interest in part because they lie beyond existing theoretical frameworks. In particular, fracton phases present fundamental challenges to common assumptions about the relationship between phases of matter and quantum field theories. In this talk, Hermele will show how carefully considering the symmetries of fracton phases — including generalized global symmetries — can help shed light on some of their mysteries. He will discuss both symmetries that emerge in the infrared and symmetries that underpin mechanisms where condensation of certain extended objects leads to a fracton phase.

Nathan Seiberg