This series consists of talks in the area of Condensed Matter.
I give an overview of work with Aasen and Mong on topologically invariant defects in two-dimensional classical lattice models, quantum spin chains and tensor networks. We show how to find defects that satisfy commutation relations guaranteeing the partition function depends only on their topological properties. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. These lattice topological defects have a variety of useful applications.
Large deviation theory gives a general framework for studying nonequilibrium systems which in many ways parallels equilibrium thermodynamics. In transport, according to the large deviation principle, the distribution of rare fluctuations of the total transfer (of charge, energy, etc.) between two baths take a special form encoded by the large deviation function, which plays the role of a free energy. Its Legendre transform is the scaled cumulant generating function (SCGF).
I will present recent results (with Zhen Bi) on novel quantum criticality and a possible field theory duality in 3+1 spacetime dimensions. We describe several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D. We present situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility - which we dub “unnecessary quantum critical points” - of stable generic continuous phase transitions within the same phase.
Many-body localization generalizes the concept of Anderson localization (i.e. single particle localization) to isolated interacting systems, where many-body eigenstates in the presence of sufficiently strong disorder can be localized in a region of Hilbert space even at nonzero temperature. This is an example of ergodicity breaking, which manifests failure of thermalization or more specifically the break down of eigenstate-thermalization hypothesis.
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.
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.
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.
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.
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.