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.

8 pages, 6 figures

References in corpus (10)

• Real time evolution using the density matrix renormalization group
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Subwavelength vacuum lattices and atom-atom interactions in photonic crystals
• Dynamical crystallization in a low-dimensional Rydberg gas
• An experimental and theoretical guide to strongly interacting Rydberg gases
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Many-body theory of non-equilibrium systems
• Preparation and detection of magnetic quantum phases in optical superlattices

Cited by in corpus (5)

• Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
• Nonequilibrium dynamics of spin-boson models from phase space methods
• Relaxation of the collective magnetization of a dense 3D array of interacting dipolar S=3 atoms
• The effect of active photons on dynamical frustration in cavity QED
• Fragility to quantum fluctuations of classical Hamiltonian period doubling