Quantum chaos challenges many-body localization
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.
quantum statistical mechanics
quantum chaos
kvantna statistična mehanika
kvantni kaos
true
false
false
Angleški jezik
Slovenski jezik
Neznano
2021-01-13 14:09:37
2021-01-13 14:09:38
2021-04-20 13:28:08
0000-00-00 00:00:00
2020
0
0
Str. 062144-1-062144-12
iss. 6
Vol. 102
2020
0000-00-00
PostprintKoncna
Objavljeno
NiDoloceno
536.93
2470-0045
10.1103/PhysRevE.102.062144
46785795
2048366611
RAZ_Suntajs_Jan_2020.pdf
RAZ_Suntajs_Jan_2020.pdf
1
1AEE6E20502D97E64980538EB703509C
7a81e90c90aa7441b8686013c960ebd72c79fdc644490582c809d94a78202642
8532a385-a1bb-11eb-a523-00155dcfd717
https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=139679
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.062144
1
https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=140132
Fakulteta za matematiko in fiziko