Quantum Matter

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.

Already in their early papers, Kosterlitz and Thouless envisaged the melting of solids by the unbinding of the topological defects associated with translational order: dislocations. Later it was realized that the resulting phases have translational symmetry but rotational rigidity: they are liquid crystals.

We consider the topological melting of solids as a zero-temperature quantum phase transition. In a generalization of particle-vortex duality, the Goldstone modes of the solid, phonons, map onto gauge bosons which mediate long-range interactions between dislocations. The phase transition is achieved by a Bose-Einstein condensation of dislocations, restoring translational symmetry and destroying shear rigidity. The dual gauge fields become massive due to the Anderson-Higgs mechanism. In this sense, the liquid crystal is a "stress superconductor".

We have developed this dual gauge field theory both in 2+1D, where dislocations are particle-like and phonons are vector bosons, and 3+1D where dislocations are string-like and phonons are Kalb-Ramond gauge fields. Focussing mostly on the theoretical formalism, I will discuss the relevance to recent experiments on helium monolayers, which show evidence for a quantum hexatic phase.

References:

2+1D : Physics Reports 683, 1 (2017)

3+1D : Physical Review B 96, 1651115 (2017)

Topology has in the past decades become an organizing principle in the classification and characterization of phases of matter.  While all possible topological phases of free fermions in the presence of external symmetries have been fully worked out, the inclusion of lattice symmetries relevant to any real-life material provides for an active research area.

In this seminar, I will present a classification of all possible gapped topological phases of non-interacting insulators with lattice symmetries, both in the absence and presence of time-reversal symmetry. This is done using a very simple counting scheme based on the electronic band structure of the materials. Despite the simplicity of the procedure, it is based on (and matches all known predictions of) the far more involved mathematical framework known as K-theory, which establishes the correctness and completeness of the counting scheme. The same straightforward counting can also be used to study transitions between crystalline topological phases. This allows us to list all possible types of such transitions for any given crystal structure, and accordingly stipulate whether or not they give rise to intermediate Weyl semimetallic phases. The presented procedure is ideally suited for the analysis of real, known materials, as well as the prediction of new, experimentally relevant, topological materials.

References:

http://doi.org/10.1103/PhysRevX.7.041069

http://arxiv.org/pdf/1711.04769

Quantum field theories play an important role in many condensed matter systems for their description at low energies and long length scales. In 1+1 dimensional critical systems the energy spectrum and the spectrum of scaling dimensions are intimately related in the presence of conformal symmetry. In higher space-time dimensions this relation is more subtle and not well explored numerically. In this talk we motivate and review our recent effort to characterize 2+1 dimensional quantum field theories using computational techniques 2+targetting the energy spectrum on a spatial torus. We discuss several examples ranging from the O(N) Wilson Fisher theories and Gross-Neveu-Yukawa theories to deconfinement- confinement transitions in the context of topological ordered systems. We advocate a phenomenological picture that provides insight into the operator content of the critical field theories.

The strong interaction of quarks and gluons is described theoretically within the framework of Quantum Chromodynamics (QCD). The most promising way to evaluate QCD for all energy ranges is to formulate the theory on a 4 dimensional Euclidean space-time grid, which allows for numerical simulations on state of the art supercomputers. We will review the status of lattice QCD calculations providing examples such as the hadron spectrum and the inner structure of nucleons. We will then point to problems that cannot be solved by conventional Monte Carlo simulation techniques, i.e. chemical potentials and understanding the large amount of charge and parity symmetry violation. It will be demonstrated at the example of the 1+1 dimensional Schwinger model that tensor network techniques are able to overcome these problems opening thus a possible path for a solution also in QCD.