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Quantum chaos challenges many-body localization
Jan Šuntajs, Janez Bonča, Tomaž Prosen, Lev Vidmar, 2020

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.
Keywords: kvantna statistična mehanika, kvantni kaos, quantum statistical mechanics, quantum chaos
DiRROS - Published: 13.04.2021; Views: 5; Downloads: 2
URL Fulltext (0,00 KB)

Varna interoperabilna infrastruktura za pametna mesta
Blaž Ivanc, Dušan Gabrijelčič, Borka Jerman-Blažič, 2015

DiRROS - Published: 08.12.2020; Views: 210; Downloads: 65
.pdf Fulltext (722,01 KB)

Storitve prožnosti prorabnikov za upravljanje pametnih omrežij
Dušan Gabrijelčič, Arso Savanović, Damijan Bobek, 2015

DiRROS - Published: 08.12.2020; Views: 219; Downloads: 65
.pdf Fulltext (234,43 KB)

Towards managerial support for data analytics results
Uroš Bole, Gregor Papa, 2020

DiRROS - Published: 24.11.2020; Views: 204; Downloads: 114
.pdf Fulltext (215,38 KB)

Simulation of variational Gaussian process NARX models with GPGPU
Tadej Krivec, Gregor Papa, Juš Kocijan, 2020

DiRROS - Published: 24.11.2020; Views: 213; Downloads: 99
.pdf Fulltext (788,32 KB)

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