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arXiv:1207.1861 · Physica E Low-dimensional Systems and Nanostructures

The excitation operator method and its application to spin dynamics in the one-dimensional XXZ model

Pei Wang

Published Nov 9, 2012• 5 citations
arXivHTMLPDF
DOI
10.1016/j.physe.2012.10.032

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We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator, which, as opposed to most quantum Monte Carlo methods, makes it possible to access the dynamics at longer times. The Monte Carlo trajectories are realized through a piecewise stochastic-deterministic reversible evolution where free dynamics is interspersed with two-process quantum jumps. The dynamical sign problem is bypassed via the so-called deadweight approximation, which stabilizes the many-body phases at longer times. We benchmark our method by simulating spin excitation propagation in the one-dimensional (1D) XXZ spin chain, dynamical confinement in the 1D quantum Ising model and quenched magnetization dynamics in the two-dimensional square Ising model. Finally, we also show how to extract dynamical information directly from the Laplace representation.