Simulation of quantum spin dynamics by phase space sampling of Bogoliubov-Born-Green-Kirkwood-Yvon trajectories

Lorenzo Pucci, Analabha Roy, and Michael Kastner
Phys. Rev. B 93, 174302 – Published 4 May 2016

Abstract

A numerical method, suitable for the simulation of the time evolution of quantum spin models of arbitrary lattice dimension, is presented. The method combines sampling of the Wigner function with evolution equations obtained from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Quantum correlations are treated through both the Wigner function sampling and the BBGKY evolution, bringing about highly accurate estimates of correlation functions. The method is particularly suitable for long-range interacting systems, and we demonstrate its power by comparing with exact results as well as other numerical methods. As an application we compute spin squeezing in a frustrated two-dimensional lattice with antiferromagnetic power-law interactions and a transverse field, making predictions pertinent to future ion trap experiments.

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  • Received 13 October 2015
  • Revised 12 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.174302

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Lorenzo Pucci1, Analabha Roy1, and Michael Kastner1,2,*

  • 1National Institute for Theoretical Physics, Stellenbosch 7600, South Africa
  • 2Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa

  • *kastner@sun.ac.za

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Issue

Vol. 93, Iss. 17 — 1 May 2016

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