Exploring many-body localization and thermalization using semiclassical methods

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.

We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying (1/r α ) interactions. We focus on two spin-1/2 Hamiltonians featuring power-law interactions: Heisenberg and XY and characterize their corresponding long-time dynamics using three distinct diagnostics: decay of a staggered magnetization pattern I(t), growth of entanglement entropy S(t), and growth of quantum Fisher information FQ(t). For sufficiently rapidly decaying interactions α > αc we find a many-body localized phase, in which I(t) saturates to a non-zero value, entanglement entropy grows as S(t) ∝ t 1/α , and Fisher information grows logarithmically. Importantly, entanglement entropy and Fisher information do not scale the same way (unlike short range interacting models). The critical power αc is smaller for the XY model than for the Heisenberg model.

Ultracold polar molecules are an ideal platform for studying many-body physics with long-range dipolar interactions. Experiments in this field have progressed enormously, and several groups are pursuing advanced apparatus for manipulation of molecules with electric fields as well as single-atomresolved in situ detection. Such detection has become ubiquitous for atoms in optical lattices and tweezer arrays, but has yet to be demonstrated for ultracold polar molecules. Here we present a proposal for the implementation of site-resolved microscopy for polar molecules, and specifically discuss a technique for spin-resolved molecular detection. We use numerical simulation of spin dynamics of lattice-confined polar molecules to show how such a scheme would be of utility in a spindiffusion experiment.