Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented Truncated Wigner method

TL;DR

This paper introduces an augmented Truncated Wigner Approximation (TWA) that captures many-body quantum interference effects in chaotic bosonic systems by incorporating symmetry considerations, extending the classical-like TWA to include genuine quantum phenomena.

Contribution

The authors develop a modified TWA method that accounts for symmetry-induced quantum interference, enabling more accurate modeling of many-body quantum effects in chaotic bosonic systems.

Findings

The augmented TWA successfully captures interference effects related to symmetries.

The method is validated in Bose-Hubbard models with chaotic dynamics.

Additional many-body interference phenomena are revealed using the new approach.

Abstract

Although highly successful, the Truncated Wigner Approximation (TWA) does not account for genuine many-body quantum interference between different solutions of the mean-field equations of a bosonic many-body (MB) system. This renders the TWA essentially classical, where a large number of particles formally takes the role of the inverse of Planck's constant $\hbar$. The failure to describe genuine interference phenomena, such as localization and scarring in Fock space, can be seen as a virtue of this quasiclassical method, which thereby allows one to identify genuine quantum effects when being compared with "exact" quantum calculations that do not involve any a priori approximation. A rather prominent cause for such quantum effects that are not accounted for by the TWA is the constructive interference between the contributions of symmetry-related trajectories, which would occur in the presence of discrete symmetries provided the phase-space distribution of the initial state and the observable to be evaluated feature a strong localization about the corresponding symmetry subspaces. Here we show how one can conceive an augmented version of the TWA which can account for this particular effect. This augmented TWA effectively amounts to complementing conventional TWA calculations by separate Truncated Wigner simulations that are restricted to symmetric subspaces and involve weight factors that account for the dynamical stability of sampling trajectories with respect to perpendicular deviations from those subspaces. We illustrate the validity of this method at pre- as well as post-Ehrenfest time scales in prototypical Bose-Hubbard systems displaying chaotic classical dynamics, where it also reveals the existence of additional MB interference effects.