Date: 6/9/2021
Time: 15:00 (Taipei time), 16:00 (Tokyo time)
Venue: Zoom [Registration] is required
Speaker: Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)
Title: Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy
Abstract:
The Berezinskii-Kosterlitz-Thouless (BKT) transition was historically the first example of topological phase transitions. Here we re-investigate the BKT transition in the 2D classical XY model, combining the Tensor Network Renormalization (TNR) and the Level Spectroscopy method based on the finite-size scaling of the Conformal Field Theory. By systematically analyzing the spectrum of the transfer matrix of the systems of various moderate sizes which can be accurately handled with a finite bond dimension, we determine the critical point removing the logarithmic corrections. This improves the accuracy by an order of magnitude over previous studies including those utilizing TNR. Our analysis also gives a visualization of the celebrated Kosterlitz Renormalization Group flow based on the numerical data.
Reference: Atsushi Ueda and M.O., arXiv:2105.11460
Date: 5/19/2021
Time: 20:00 (Taipei time), 08:00 (Toronto time)
Venue: Zoom [Registration] is required
Speaker: Juan Carrasquilla (Vector Institute for Artificial Intelligence)
Title: Variational Neural Annealing
Abstract:
Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for ground state solutions of a target Hamiltonian. While powerful, simulated annealing is known to have prohibitively slow sampling dynamics when the optimization landscape is rough or glassy. In this talk I will show that by generalizing the target distribution with a parameterized model, an analogous annealing framework based on the variational principle can be used to search for ground state solutions. Autoregressive models such as recurrent neural networks provide ideal parameterizations since they can be exactly sampled without slow dynamics even when the model encodes a rough landscape. We implement this procedure in the classical and quantum settings on several prototypical spin glass Hamiltonians, and find that it significantly outperforms traditional simulated annealing in the asymptotic limit, illustrating the potential power of this yet unexplored route to optimization.
Date: 4/28/2021
Time: 12:30 (Taipei time), 14:30 (Briesbane time)
Venue: Zoom [Registration] is required
Speaker: Ian McCulloch (University of Queensland)
Title: Finite-entanglement scaling functions at quantum critical points
Abstract:
For translationally invariant infinite MPS, finite entanglement scaling has emerged as a powerful alternative that has many advantages over finite-size scaling for the calculation of critical phenomena. I will give an overview of the ideas behind finite entanglement scaling, and discuss in detail approaches using higher moments, leading to the infinite-size version of the 4th order (Binder) cumulant. By choosing appropriate cumulant ratios, critical points can be determined without the need to use the bond dimension as a scaling parameter, which is a major advantage over earlier approaches. The scheme also applies to quantities that are not normally regarded as local order parameters, such as time reversal and spatial inversion, which allows the quick and accurate determination of critical points separating symmetry-protected phases.