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

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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.

Keywords:quantum statistical mechanics, quantum chaos
Tipology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Number of pages:Str. 062144-1-062144-12
Numbering:Vol. 102, iss. 6
ISSN on article:2470-0045
DOI:10.1103/PhysRevE.102.062144 This link opens in a new window
COBISS.SI-ID:46785795 This link opens in a new window
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Record is a part of a journal

Title:Physical review
Shortened title:Phys. rev., E
Publisher:American Physical Society
COBISS.SI-ID:2048366611 This link opens in a new window

Document is financed by a project

Funder:EC - European Commission
Funding Programme:H2020
Project no.:694544
Name:Open Many-body Non-Equilibrium Systems

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:P1-0044
Name:Teorija trdnih snovi in statistična fizika

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:P1-0402
Name:Matematična fizika

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:J1-1696
Name:Diagnoza neravnovesne kvantne materije

Secondary language

Keywords:kvantna statistična mehanika, kvantni kaos

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