ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Yusipov I. I., Kozinov E. A., Laptyeva T. V. Transition from ergodic to many-body localization regimes in open quantum systems in terms of the neural-network ansatz. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 3, pp. 268-275. DOI: 10.18500/0869-6632-2022-30-3-268-275

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Transition from ergodic to many-body localization regimes in open quantum systems in terms of the neural-network ansatz

Yusipov Igor I., Lobachevsky State University of Nizhny Novgorod
Kozinov Evgeniy Aleksandrovich, Lobachevsky State University of Nizhny Novgorod
Laptyeva Tatjana Vladimirovna, Lobachevsky State University of Nizhny Novgorod

The purpose of our work is to investigate asymptotic stationary states of an open disordered many-body quantum model which is characterized by an ergodic — many-body localization (MBL) phase transition. To find these states, we use the neural-network ansatz, a new method of modeling complex many-body quantum states discussed in the recent literature. Our main result is that that the ergodic phase — MBL transition is detectable in the performance of the neural network that is trained to reproduce the asymptotic states of the model. While the network is able to reproduce, with a relatively high accuracy, ergodic states, it fails to do so when the model system enter the MBL phase. We conclude that MBL features of the model translate into the cost function landscape which becomes corrugated and acquires many local minima.

This work was supported by Russian Foundation for Basic Research and the Government of the Nizhni Novgorod region of the Russian Federation, grant No. 18-41-520004
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