2019/12/22 by Samuel E. Begg, S. E. Begg, A. G. Green +1 · 8 citations
Computer Science · Physics and Astronomy · #Hermitian matrix #Law #Model Reduction and Neural Networks #Observable #Physics #Quantum #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Representation (politics) #Spins #Statistical physics #Stochastic differential equation #Time evolution #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · open access · doi:10.1088/1751-8121/abbf87
published in Journal of Physics A Mathematical and Theoretical 53(50), 50LT02 (Institute of Physics) · 5 pages, 4 figures, Supplementary Material
arxiv created 2019/12/22 · openalex publication_date 2020/10/08 · openalex created_date 2020/10/15 · arxiv updated 2020/12/30 · openalex updated_date 2026/08/05
Abstract We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained, including two-dimensional systems with up to 49 spins. We demonstrate that the results for physical observables are in excellent agreement with exact results and alternative numerical techniques where available. We further develop a hybrid stochastic approach involving matrix product states. In the presence of finite numerical sampling, we show that the non-Hermitian character of the stochastic representation leads to the growth of the norm of the time-evolving quantum state and to departures for physical observables at late times. We demonstrate approaches that correct for this and discuss the prospects for further development.