Quantum chaos challenges many-body localization
Šuntajs, Jan (Author), Bonča, Janez (Author), Prosen, Tomaž (Author), Vidmar, Lev (Author)

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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 $g=\mathrm{log}_{10}(t_H/t_{Th})$, which is defined through the ratio of two characteristic many-body time scales, the Thouless time $t_{Th}$ and the Heisenberg time $t_H$, 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, $t_{Th} \approx t_H$, 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.

Language: English quantum statistical mechanics, quantum chaos 1.01 - Original Scientific Article FMF - Faculty of Mathematics and Physics 2020 Str. 062144-1-062144-12 Vol. 102, iss. 6 536.93 2470-0045 10.1103/PhysRevE.102.062144 46785795 152 158 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Physical review Phys. rev., E American Physical Society 2470-0045 2048366611

## Document is financed by a project

Funder: EC - European Commission H2020 694544 Open Many-body Non-Equilibrium Systems OMNES

Funder: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS) P1-0044 Teorija trdnih snovi in statistična fizika

Funder: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS) P1-0402 Matematična fizika

Funder: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS) J1-1696 Diagnoza neravnovesne kvantne materije

## Secondary language

Language: Slovenian kvantna statistična mehanika, kvantni kaos