MPS Conference on Ultra Quantum Matter II

The meeting opened with brief introductory remarks from Gregory Gabadadze, who also congratulated the three winners of the 2018 Dirac Medal (Sachdev, Son and Wen), all of whom were participants in the conference. The scientific program was kicked off by Leon Balents who analyzed a remarkable new experiment on the conduction of heat in a quantum magnet, RuCl3, and argued convincingly that it strongly supported a remarkable type of topological field theory – a Chern-Simons theory with a non-Abelian gauge potential, that describes excitations with a generalization of the usual Bose-Fermi statistics, captured by a non-Abelian group. That these states would occur under these conditions was first proposed by Alexei Kitaev, and they hold promise for emerging efforts to build a topological qubit, a protected quantum memory which may be useful for quantum computing.

Michael Levin presented a rigorous theorem on one-dimensional spin systems, showing that such models with an Ising symmetry must either have a local order parameter or a string order parameter in gapped phases. This result puts rigorous constraints on the boundary physics of two-dimensional topologically ordered phases. In particular, it shows that the toric code model has exactly two types of gapped boundaries. Moreover, this result can be used to show that certain topological orders necessarily have gapless boundaries.

A recurring theme of the meeting was the recently discovered non-supersymmetric dualities, which has led to rapid developments both on the condensed matter and field theory ends. Talks by Karch, Seiberg and Senthil described in detail our current understanding of the subject and laid out the many interesting phenomena that can arise in and be explained by the study of these duality symmetries. They also discussed recent attempts to move beyond 2+1D Dualities.

Subir Sachdev gave an intriguing talk on signatures of topology and gauge structures in the spectrum of the Sachdev Ye Kitaev (SYK) model. He argued that the large ground state degeneracy was reminiscent of topological sectors, and described the theory that counts these states. Feedback at the meeting led to new ideas on how to numerically identify these sectors in the SYK model, which is now being implemented. He also spoke about applications of gauge theories to the high temperature cuprate superconductors. The talks on new phases of gauge theories by Seiberg and Senthil led to a new approach to analyzing these gauge theories near the optimal doping critical point.

Juan Maldacena gave a very stimulating talk from an outsider’s perspective. Maldacena’s groundbreaking work from two decades ago relates particular quantum gravitational theories to the dynamics of strongly coupled field theories. He summarized an ambitious program that relates the advances in the study of ultra quantum matter pursued by the other speakers to interesting questions in quantum gravity, giving an interesting new perspective on both those topics.

John McGreevy discussed the entanglement structure of ultra-quantum states of matter, describing how various ultra-quantum states can be constructed using quantum circuits with a renormalization group structure. Entanglement properties of the state are then reflected in characteristics of the quantum circuit. These results have implications for quantum simulations where one implements a quantum circuit in the lab to build a many-body quantum state, such as the emerging technique of variational quantum simulation discussed in Peter Zoller’s talk. Zoller presented theoretical and experimental results on a simulation of the one-dimensional Schwinger model; similar techniques may able to realize a variety of ultra-quantum states in the near future. Zoller also showed how implementing random unitaries can help in the measurement of exotic and non-local correlations such as Renyi entropy and `out of time order’ correlation functions, which are vital to diagnosing new states of matter. These ideas open up the possibility of realistically measuring these novel correlators in many particle quantum systems. In his talk reporting recent experimental results at Harvard, Marcus Greiner showed how exquisite control over ultra-cold atoms is now possible in the Fermi gas microscope, and new signatures of doped atoms into an antiferromagnetic background can be extracted, which have never before been visualized.

Pablo Jarillo-Herrero reported on experiments in twisted bilayer graphene. When two sheets of graphene are twisted relative to one another by 1 degree, a `magic angle’ previously predicted by theorists, superconductivity emerges, a recent experimental discovery that has taken the condensed matter community by storm. Ashvin Vishwanath reported on the surprising topological properties of magic angle graphene and attempts to model the insulating and superconducting phases, which were the results of a collaboration initiated with T. Senthil at the previous (Ultra-Quantum Matter I) Simons conference.

Leon Balents
UC Santa Barbara

Ultra-Quantum Matter, from Theory to Experiment

Ultra-quantum matter brings together many communities of theoretical research, from mathematical physicists to condensed matter and atomic theorists to string theorists. This talk will focus on how it connects to experimental studies and discuss promising examples of the latter and the questions they raise.

Pablo Jarillo-Herrero
MIT

Magic Angle Graphene: A New Platform for Strongly Correlated Physics

The understanding of strongly correlated quantum matter has challenged physicists for decades. Such difficulties have stimulated new research paradigms, such as ultra-cold atom lattices for simulating quantum materials. In this talk, I will present a new platform to investigate strongly correlated physics, based on graphene moiré superlattices. In particular, I will show that when two graphene sheets are twisted by an angle close to the theoretically predicted ‘magic angle,’ the resulting flat band structure near the Dirac point gives rise to a strongly-correlated electronic system. These flat bands exhibit half-filling insulating phases at zero magnetic field, which we show to be a correlated insulator arising from electrons localized in the moiré superlattice. Moreover, upon doping, we find electrically tunable superconductivity in this system, with many characteristics similar to high-temperature cuprates superconductivity. These unique properties of magic-angle twisted bilayer graphene open up a new playground for exotic many-body quantum phases in a 2-D platform made of pure carbon and without magnetic field. The easy accessibility of the flat bands, the electrical tunability and the bandwidth tunability though twist angle may pave the way toward more exotic correlated systems, such as quantum spin liquids or correlated topological insulators.

Andreas Karch
University of Washington

Dualities in 2+1 Dimensions and Beyond

After a brief review of the flurry of recent developments regarding dualities in 2+1 dimensions, I’ll describe our progress toward using these novel dualities to gain insights into 3+1 and 1+1 dimensional physics. In particular, I’ll show that the strong-weak coupling duality of maximally supersymmetric gauge theories in 3+1 dimensions, as well as bosonization in 1+1 dimensions, can be derived from well-known 2+1 dimensional dualities.

Michael Levin
University of Chicago

Constraints on Order and Disorder Parameters in Quantum Spin Chains and Applications

I will discuss a theorem that shows that a gapped ground state of an Ising symmetric quantum spin chain must have either a nonzero order parameter or a nonzero disorder parameter. I will also discuss an application of this theorem to understanding the stability/instability of gapless edge modes of a large class of two-dimensional topological phases.

Juan Maldacena
Princeton University

Traversable Wormholes

We discuss how the coupling of two SYK models by simple operators gives rise to a gapped state that displays many features of the approximate SL(2) conformal symmetry of the theory. The configuration is related to traversable wormholes in gravity. We will further show how the intuition generated by solving this model leads to an interesting solution describing a traversable wormhole in four dimensions.

John McGreevy
UC San Diego

Hierarchical Growth of Entangled States, or s-sourcery

This talk will describe the s-sourcery program, an attempt to extend the lessons of the renormalization group to quantum many-body states. Outcomes so far include a classification axis for states of matter, a proof of the area law for entanglement entropy of subregions (under mild assumptions) and a new algorithm for constructing efficiently contractible tensor network representations of ground states. I’ll describe recent progress on implementing this algorithm.

Subir Sachdev
Harvard University

Gauge Theories of Ultra-Quantum Metals

Metals with local antiferromagnetic spin correlations can be conveniently described by transforming to a rotating reference frame in spin space, leading to a theory with an emergent SU(2) gauge field. The Higgs phases of such a theory will be compared with numerical cluster-DMFT studies of the lightly doped square lattice Hubbard model. The Higgs phases can also help understand recent photoemission observations in the electron-doped cuprate NCCO, which detected a reconstruction gap in the electronic dispersion at a doping where there is no antiferromagnetic order. The transitions out of the Higgs phases into confining phases are promising routes to understanding the strange metal behavior seen at optimal and over-doping, after including the effects of disorder. I will discuss models of strange metals built out of SYK islands, including cases with emergent gauge fields.

Nathan Seiberg
Institute for Advanced Study

Recent Advances in 2+1d QFT

We will review recent developments in the study of quantum field theory in 2+1 dimensions. Newly discovered subtleties in the analysis of the short-distance behavior of these theories have uncovered surprising properties. They help motivate a rich web of conjectures about the long-distance behavior of these systems. These conjectures describe new phases and new-phase transitions between them. Also, in many cases, these transitions have several different dual descriptions. These new developments were motivated by ideas in high-energy physics, string theory and condensed matter physics. And they have potential applications in these fields.

T. Senthil
MIT

Quantum Criticality, Topology and Dualities

I will describe recent progress in our understanding of unusual quantum critical points that lie outside the standard Landau paradigm. Crucial recent theoretical input into these quantum critical points has come from the study of gapped topological phases of matter and from the understanding of dualities of quantum field theories. I will highlight these connections and describe several new results on quantum critical points in 3+1 dimensional systems.

Ashvin Vishwanath
Harvard University

Modeling Correlated Phenomena in Twisted Bilayer Graphene

The recent discovery of superconductivity and Mott insulators in twisted bilayer graphene and related materials points to the importance of correlation effects in this new solid state physics platform. An interesting and potentially crucial ingredient is band topology inherited from the Dirac fermion dispersion of graphene. We will discuss our theoretical efforts to model these systems and study the resulting ground states with interactions. We find that key aspects of the physics differ from previously studied correlated superconductors.

Peter Zoller
Center for Quantum Physics, University of Innsbruck, and
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck

Quantum Simulation with Cold Atoms and Ions

Zoller will discuss recent developments in quantum simulation of quantum many-body systems with atomic platforms from a theory perspective. Systems of interests include atoms in optical lattices, Rydberg atoms in optical tweezer arrays, and trapped ions. Quantum simulation has so far been discussed as analog simulation, where we physically build a system with the desired Hamiltonian; or as digital quantum simulation, where time evolution of a many-body system is represented as a sequence of quantum gates on a quantum computer. Zoller will add to this variational quantum simulation, based on a quantum feedback loop between a classical computer and an analog quantum simulator, which acts as a quantum co-processor. As an example, he will present results from an ongoing theory – experiment collaboration in Innsbruck: here our quantum resource is an analog quantum simulator with trapped ions, representing a transverse Ising model, and we compute on the quantum device the ground and excited state wave functions of the Lattice Schwinger Model as 1D QED. Remarkably, variational quantum simulation allows "self-verification" of quantum results on the quantum machine. As a second topic we will discuss novel measurement protocols for Rényi entropies, and for out-of-time-ordered correlation functions (OTOCs), which can be extracted from on statistical correlations between randomized measurements. Zoller will show a recent experiment with a (single) ion chain demonstrating experimental observation of entanglement entropies in quench dynamics. He will conclude his talk with a brief outlook on possible future directions, including sub-wavelength optical lattices for atomic Hubbard models, and quantum chemistry.