A generalized phase space approach for solving quantum spin dynamics

Abstract

Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum manybody systems are key for advancing our capability to harness and understand complex quantum matter.Here we propose a new numerical approach which we refer to as generalized discrete truncated Wigner approximation (GDTWA). It is based on a discrete semi-classical phase space sampling and allows to investigate quantum dynamics in lattice spin systems with arbitrary S1/2. We show that the GDTWA can accurately simulate dynamics of large ensembles in arbitrary dimensions. We apply it for S>1/2 spin-models with dipolar long-range interactions, a scenario arising in recent experiments with magnetic atoms. We show that the method can capture beyond mean-field effects, not only at short times, but it also can correctly reproduce long time quantum-thermalization dynamics. We benchmark the method with exact diagonalization in small systems, with perturbation theory for short times, and with analytical predictions made for models which feature quantum-thermalization at long times. We apply our method to study dynamics in large S>1/2 spin-models and compute experimentally accessible observables such as Zeeman level populations, contrast of spin coherence, spin squeezing, and entanglement quantified by single-spin Renyi entropies. We reveal that large S systems can feature larger entanglement than corresponding S=1/2 systems. Our analyses demonstrate that the GDTWA can be a powerful tool for modeling complex spin dynamics in regimes where other state-of-the art numerical methods fail. case also the mean-field equations are not necessarily closed unless also intra-spin correlations are assumed to factorize. Those cases are not accounted for in the approach described here, but we will properly include them in our GDTWA method below.

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

“…Recently, a generalized TWA was proposed in [81] for the description of the dynamics of many coupled spins. In this approach, every spin is considered as a discrete variable, i.e., there is no relation to any classical phase-space.…”

“…In this approach, every spin is considered as a discrete variable, i.e., there is no relation to any classical phase-space. Thus, a set of 2 (2L + 1) 2 − 1 coupled (first-order) differential equations should be solved even for two interacting spins L. In addition, the rigid rotor evolution in external fields cannot be treated applying the technique [81].…”

Analyzing Rydberg excitation Dynamics in an atomic chain via discrete truncated Wigner approximation and artificial neural networks

“…On the other side, examples for the phase-space methods are truncated Wigner approximation (TWA) [8,9] and its discrete version (dTWA) [10][11][12], which are semi-classical approaches involving classical equations of motion for the phasespace variables. Though initially dTWA was developed for coherent spin-1/2 systems, later generalized to higher spin systems [13], higher dimensional phase space [14] and dissipative systems [15]. dTWA is recently employed to study large spin systems in which dynamical phase transitions are explored [16].…”

Generalized Discrete Truncated Wigner Approximation for Nonadiabtic Quantum-Classical Dynamics

“…Physicists often subsume those methods under the name of Truncated Wigner Approximations (TWA) with many family members [1][2][3][4][5][6][7][8][9][10][11] , whereas chemists usually call them mapping approaches, including the Meyer-Miller-Stock-Thoss (MMST) mapping and spin mapping (SM) [33][34][35][36][37][38] . The key idea of these methods is to sample the quantum distribution of the initial states as the Wigner quasiprobability distribution, and neglect higher-order quantum corrections of the Moyal bracket, thus rendering the evolution equations classical.…”