Quantum chaos challenges many-body localization

TLDR

Many‑body localization is the prototypical ergodicity‑breaking phenomenon in interacting quantum systems, while random‑matrix theory provides a framework for diagnosing quantum chaos and ergodicity. The authors numerically investigate spectral statistics of disordered interacting spin‑chain models that are expected to exhibit MBL. They quantify ergodicity with the indicator \(g=\log_{10}(t_{\mathrm H}/t_{\mathrm Th})\), where \(t_{\mathrm Th}\) is the Thouless time and \(t_{\mathrm H}\) the Heisenberg time, analogous to the dimensionless conductance in Anderson localization. Their results show that the ergodicity‑breaking transition occurs when \(t_{\mathrm Th}\approx t_{\mathrm H}\) and \(g\) becomes size‑independent, with a BKT‑type scaling that locates the crossing point and finite‑size flows toward the chaotic regime.

Abstract

Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, which represent prototype models expected to exhibit MBL. We study the ergodicity indicator $g={log}_{10}({t}_{\mathrm{H}}/{t}_{\mathrm{Th}})$, which is defined through the ratio of two characteristic many-body time scales, the Thouless time ${t}_{\mathrm{Th}}$ and the Heisenberg time ${t}_{\mathrm{H}}$, and hence resembles the logarithm of the dimensionless conductance introduced in the context of Anderson localization. We argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, ${t}_{\mathrm{Th}}\ensuremath{\approx}{t}_{\mathrm{H}}$, and $g$ becomes a system-size independent constant. Hence, the ergodicity breaking transition in many-body systems carries certain analogies with the Anderson localization transition. Intriguingly, using a Berezinskii-Kosterlitz-Thouless correlation length we observe a scaling solution of $g$ across the transition, which allows for detection of the crossing point in finite systems. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.