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arXiv:1912.10551 · Journal of Physics A Mathematical and Theoretical

Fluctuations and non-Hermiticity in the stochastic approach to quantum spins

Samuel E. Begg, Andrew G. Green, M. J. Bhaseen

Published Oct 8, 2020• 8 citations
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Abstract

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.

DOI
10.1088/1751-8121/abbf87

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We reformulate the full quantum dynamics of spin systems using a phase-space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. This representation is superior in practice to an earlier phase-space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times severalfold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse-field Ising model in one and two dimensions.
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