Talks

Docker provides "containerization" for software -- a way to package up a piece of software and all its dependencies, so that it can run the same way on different computers.  It is a promising technology for scientists, both for reproducibility, ease of collaboration, and for running software on different computers (like your laptop and different clusters).  I will go through the why and how of using Docker.  For supercomputers (such as our Symmetry machine), Docker isn't allowed due to security issues, but the Singularity program allows users to run Docker containers, so I'll show you how to run your Docker container on Symmetry using Singularity.

A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed ‘density matrix truncation’ (DMT) to investigate the long-time dynamics of large-scale Floquet systems. By implementing a spatially inhomogeneous drive to a 1D quantum chain, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system’s dynamics. We find that DMT accurately captures two essential pieces of Floquet physics, namely prethermalization and late-time heating to infinite temperature. Moreover, we show that these two aspects are driven by different microscopic mechanisms.

We study dimensionally restricted non-perturbative causal set quantum dynamics in two and three spacetime dimensions with non-trivial global spatial topology.  The causal set sample space is generated from causal embeddings into latticisations of flat background spacetimes with global spatial topology  and  in two and three dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations via an analytic continuation of a parameter  analogous to an inverse temperature. In both two and three dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by "layered" posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. These results are similar in character to those obtained for topologically trivial causal set dynamics over the sample space of 2-orders. The current simulations use a newly developed framework for causal set MCMC calculations, and provide the first implementation of a three-dimensional causal set dynamics.

arXiv paper: https://arxiv.org/abs/1908.11647

A recent construction of HOMFLY-PT knot homology by Oblomkov-Rozansky has its physical origin in “B-twisted” 3D N=4 gauge theory, with adjoint and fundamental matter. Mathematically, the construction uses certain categories of matrix factorization. We apply 3D Mirror Symmetry to identify an A-twisted mirror of this construction. In the case of algebraic knots, we find that knot homology on the A side gets expressed as cohomology of affine Springer fibers (related but not identical to work if Gorsky-Oblomkov-Rasmussen-Shende). More generally, we propose a Fukaya-Seidel category mirror to the Oblomkov-Rozansky matrix factorization. Joint work with N Garner, J Hilburn, A Oblomkov, and L Rozansky.

Black holes in the background of the AdS soliton are, according to the gauge/gravity correspondence, dual to droplets of deconfined plasma surrounded by a confining vacuum. In this talk I will present, for the first time, the real time dynamics of finite energy black holes in these backgrounds. We consider horizonless initial data sourced by a massless scalar field. Upon time evolution, prompt scalar field collapse produces an excited black hole that eventually settles down to equilibrium at the bottom of the AdS soliton. Radiation in these backgrounds is carried by a set of massive states that, in the dual field theory, can be interpreted as particles. Thus, our results are relevant to describe the out-of-equilibrium dynamics in strongly coupled gauge theories that exhibit confinement. This is work in progress in collaboration with Hans Bantilan and David Mateos.

 Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the boundary. In this work, we combine HQECC with Hamiltonian simulation theory to construct a bulk-boundary mapping between local Hamiltonians, whilst retaining all the features of the HQECC duality. This allows us to construct a duality between models, encompassing the relationship between bulk and boundary energy scales and time dynamics.

It also allows us to construct a map in the reverse direction: from local boundary Hamiltonians to the corresponding local Hamiltonian in the bulk. Under this boundary-to- bulk mapping, the bulk geometry emerges as an approximate, low-energy, effective theory living in the code-space of an (approximate) HQECC on the boundary. At higher energy scales, this emergent bulk geometry is modified in a way that matches the toy models of black holes proposed previously for HQECC. Moreover, the duality on the level of dynamics shows how these toy-model black holes can form dynamically.

We will talk about recent progress in NMR technologies simulating topological phases. We will describe how states are prepared, how they are evolved in time and various tricks that we can play with it, including measurements of topological properties such as modular matrices, and thus potentially applied for identifying phases of matter in future simulations.