Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space

Abstract

Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one-and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.

Continuous phase-space methods on discrete phase spaces

“…Importance of the initial condition sampling and a comparison of continuous and discrete distributions was discussed in [27]. However, the derivation in [27] is valid only for Wigner functions of spin 1/2 systems and is based on a product-probability assumption, which results in a truncated Wigner-type approximation not permitting a systematic expansion or application to open quantum systems.…”

“…This identification enables to combine sampling of the initial state in the discrete phase-space and continuous simulation in the SU (N ) phase space [27]. Further, continuous phase-space methods enable a systematic expansion in the quantum noise parameter [11,12] and extension to the dissipative models [11].…”

“…However, the derivation in [27] is valid only for Wigner functions of spin 1/2 systems and is based on a product-probability assumption, which results in a truncated Wigner-type approximation not permitting a systematic expansion or application to open quantum systems. The approach presented here is valid for any N , any s-ordered quasiprobability distribution and the generalised positive-P function, enables a systematic expansion in the noise terms, and is applicable to open quantum systems.…”

“…This identification provides a formal justification of Monte-Carlo methods on finite dimensional phase spaces proposed in [27,28], their systematic expansion beyond the semiclassical (truncated Wigner) approximation [12,29] and extension to open quantum systems. Hence, the revealed relation between continuous and discrete phase spaces should be relevant to further development of contemporary phase-space methods for simulation of long-range many-body quantum systems.…”

Nonequilibrium dynamics of spin-boson models from phase-space methods

“…Phase space methods such as the Truncated Wigner Approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [1]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations [2] to our coupled spin-boson model.…”