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

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.

Semiclassical roots of universality in many-body quantum chaos

“…This concept naturally requires a classical limit, and is intriguing because it indicates deviations from ergodicity for a fully chaotic system that globally shows eigenstate thermalization, and must be differentiated from the aforementioned quantum states localized in regular regions. Very recently, scarring in Heller's original sense could be demonstrated for an MB Bose-Hubbard system with a high-dimensional associated classical phase space, including the corresponding generalization of the scar criterion [239]. Earlier, MB 'scars', reflected in persistent oscillations of local observables, were observed in Rydberg-based quantum simulators [235], as well as in corresponding numerical simulations [39,240].…”

Genuine Many-Body Quantum Scars along Unstable Modes in Bose-Hubbard Systems

“…The likelihood for scarring increases when approaching the maximally imbalanced limit due to ever shorter periods T. This is demonstrated in Fig. 2(b), where we use an a priori indicator 2πχ=λ þ Σ T > 1 for periodic orbits to support quantum scars, generalizing the heuristic Heller criterion [8] for two-dimensional single-particle systems [34,35]. Here, λ þ Σ ≡ Σ > j λ j is the sum of positive stability exponents, and χ ≡ Q > j 2λ j =ðλ th þ λ j Þ is a heuristic factor to suppress close-to-regular or mixed dynamics with a threshold chosen as λ th ¼ 0.3J.…”