The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their technological exploitation. A central question in open quantum systems concerns the fate of quantum correlations, and the possibility of controlling them by engineering the competition between the Hamiltonian dynamics and the coupling to a bath. Such a question is challenging from a theoretical point of view, as numerical methods faithfully accounting for quantum correlations are either relying on exact diagonalization, limiting drastically the sizes that can be treated; or on approximations on the range or strength of quantum correlations, associated to the choice of a specific Ansatz for the density matrix. In this work we propose a new method to treat open quantum-spin lattices, based on stochastic quantum trajectories for the solution of the open-system dynamics. Along each trajectory, the hierarchy of equations of motion for many-point spin-spin correlators is truncated to a given finite order, assuming that multivariate
An example for a simulation can be found in run_simulation.m
. We refer to Ref. [1] for more information on the method. Please cite the article if you used or found the code useful.
[1] W. Verstraelen, D. Huybrechts, T. Roscilde, M. Wouters, Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories, PRX Quantum 4, 030304 (2023).