Quantum Matter

Remarkable recent experiments have observed Mott insulating behavior and superconductivity in moire superlattices of twisted bilayer graphene near a magic twist angle. However, the nature of the Mott insulator, origin of superconductivity and an effective model remain to be determined. I will present our understanding of these phenomena. We propose a Mott insulator with intervalley coherence that spontaneously breaks U(1) valley symmetry, and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hunds coupling. We also identify symmetry related features of the nearly flat bands that are key to understanding the strong correlation physics and constrain any lattice model description. First, although the charge density is concentrated on the triangular lattice sites of the moire pattern, the Wannier states of a tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat bands necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat mini-band are derived, which highlight the importance of further neighbor hopping and interactions. We discuss the consequences of this picture.

Recently, a web of quantum field theory dualities was proposed linking several problems in the study of strongly correlated quantum critical points and phases in two spatial dimensions. These dualities follow from a relativistic flux attachment duality, which relates a Wilson-Fisher boson with a unit of attached flux to a free Dirac fermion. While several derivations of members of the web of dualities have been presented thus far, none explicitly involve the physics of flux attachment, which in relativistic systems affects both statistics and spin. We discuss how this can be achieved in models of relativistic current loops, where the concept of relativistic flux attachment can be made precise. In this context, we provide simple, explicit “derivations” of members of the web of dualities. We describe some implications of this work for relativistic composite fermion theories arising in condensed matter physics, as well as new possibilities for deriving additional dualities using these techniques.

Recent quench experiments in a quantum simulator of interacting Rydberg atoms demonstrated surprising long-lived, periodic revivals from certain low entanglement states, while apparently quick thermalization from others. Motivated by these findings, I will in this talk analyze the dynamics of a family of kinetically constrained spin models related to the experiments. By introducing a manifold of locally entangled spins, representable by a low-bond dimension matrix product state (MPS), I will derive "semiclassical" equations of motion for them. I find that they host isolated, unstable periodic orbits, the presence of which captures the long-lived oscillations and gives rise to slow relaxation of local observables from certain initial configurations. This thus represents a form of weak breaking of ergodicity in dynamics. Our results are reminiscent of the phenomenon of quantum scarring in single-particle chaotic systems which is rooted in classical unstable periodic orbits, and complement the explanation of the recurrences given by [Nature Physics (2018), doi:10.1038/s41567-018-0137-5], in terms of motion over special nonergodic many-body eigenstates, suggestively dubbed `quantum many-body scars'. 

We demonstrate that extremely long range correlations may develop in systems that start from equilibrium and are then rapidly cooled (or driven in other ways). Amongst other things, these correlations suggest a collapse of the viscosity data of glass formers. This collapse is found to be obeyed over 16 decades of relaxation times in experimental data on all known types of supercooled fluids. 

Over the last decade, there have been enormous gains in machine learning technology primarily driven by neural networks. A major reason neural networks have outperformed older techniques is that the cost of optimizing them scales well with the size of the training dataset. But neural networks have the drawback that they are not very well understood theoretically.

Recent work by several groups has explored an alternative approach to creating machine learning model functions based on tensor networks, which are a technique for parameterizing many-body quantum wavefunctions. The cost of training tensor network models scales similarly to the cost of training neural networks. In addition, their relatively simple, linear structure has provided good theoretical understanding of their properties, and underpins many powerful techniques to optimize and manipulate them. 

After introducing tensor network machine learning models, I will discuss some of the techniques to optimize them and results for supervised and generative machine learning tasks. These techniques can automatically adapt the number of parameters and suggest interesting interpretations and extensions for 'deep' tensor network variants. I will conclude by discussing a recent tensor network based proposal to formulate hybrid quantum-classical algorithms for machine learning with quantum computers.

Time series data contains useful information on the phase of a system. Here we propose the use of recurrent neural networks (LSTM) to learn and extract such information in order to classify phases and locate phase boundaries. We demonstrate this on a many-body localized model, and attempt to interpret the learned behavior by looking at individual LSTM cells. We also discuss the validity of the learned model and investigate its limits.

Recently, we have shown that deep neural networks can be used to solve the Schrödinger Equation (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.042113), classical spin models (https://doi.org/10.1103/PhysRevE.97.032119), and 2d-materials such as graphene and boron-nitride (https://doi.org/10.1016/j.commatsci.2018.03.005).

I will argue that these "deep models" can be used to simulate and understand matter in a way which was not previously possible. Specifically, I will show how our recently reported extensive deep neural networks (https://arxiv.org/abs/1708.06686) can be used to infer the properties of meso-scale materials based on training data generated from much smaller structural motifs (evaluated using electronic structure methods such as density functional theory). Extensive deep neural networks scale as O(N) and can be efficiently evaluated in parallel using petascale computational platforms.

When performing numerical simulation of many-body systems we work with the goal of computing some set of averaged observables.  This process has a weakness in that, when our simulation is complete, we have no ability to determine what was the key physics that gave our result.  In this talk, I'll give a simple example, a gap in a single-particle density of states, and explain how we can use two-particle quantities to recover key 'hidden' information.  I'll then back up these claims with numerical results for the 2D Hubbard model.  For the second half of my talk I'll hope to keep your attention by introducing a parallel but MUCH more whimsical idea, unparticle physics. I'll at least TRY to explain what an unparticle is and how it might impact strongly correlated condensed matter systems.

From the Stone Age to the Silicon Age, nothing has had a more profound influence on the world than our understanding of the materials around us. The Industrial Revolution of the 19th century and the Information Revolution of the 20th were fueled by humankind’s ability to understand, harness, and control materials.

Our ongoing quest to find and develop new kinds of materials, in hopes of tackling some of society’s most challenging energy problems, requires us to learn how to build materials from the atom up. Doing so means combining state-of-the-art technologies (such as growing thin-film materials) with cutting-edge techniques for probing the electron structure. Relatively recent advances in these fields have given researchers unprecedented understanding and insight into creating new materials with exotic and useful properties.

In his public lecture at Perimeter Institute, Rob Moore will explore how the next great “age” of humankind may well be forged in this new quantum world of materials.