Wigner Cat Phases: A finely tunable system for exploring the transition to quantum chaos

TL;DR

This paper introduces Wigner Cat Phases, a tunable quantum system that transitions from chaos to a novel many-body localized regime, characterized by unique spectral features and localization phenomena.

Contribution

It proposes a new quantum model with tunable parameters to explore the transition from quantum chaos to many-body localization, revealing novel spectral and eigenstate structures.

Findings

Wigner-Dyson statistics at no selection (tuning parameter 1.0) indicating chaos.

Emergence of 'cat-ears' in spectral densities with reduced tuning, signifying localization.

Persistence of topological features without Poisson statistics, indicating a new MBL regime.

Abstract

A quantum mechanical setting consisting of a frozen qubit composed with a fully thermalized chaotic system of N states is proposed, with potential relevance to quantum control. Observing the states of the composed system selectively retaining the states leads to the observation of novel localization in the subsystem. At a tuning parameter of 1.0, implying no selection, the system exhibits Wigner-Dyson level spacing statistics, indicative of quantum chaos. As the tuning parameter is reduced and selection occurs at a cutoff, the nearest-neighbor level spacing distribution develops heavier tails, a signature of suppressed spectral mixing and the emergence of non-thermal dynamics. In these regimes, the eigendensity develops a pronounced "cat-ears" structure, reflecting the formation of spatially localized bimodal eigenstates. These topological features persist without transitioning to Poisson statistics, indicating a transition from quantum chaos to a non-thermal, novel many-body localized (MBL) regime-referred to as Wigner Cat Phases. The proposed mixed random matrix ensemble offers a practical probe for sustaining this novel quantum localization setting. Results from our rigorous spectral statistics analysis show how "cat-ears" form in spectral densities based on the degree of selection or disorder and indicate that gap ratio statistics must be used with caution in detecting the full integrable limit due to the possibility of heavy-tailed Wigner-Dyson distributions.