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

For citation:

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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Language: 
English
Heading: 
Nonlinear Dynamics and Neuroscience
Article type: 
Short communication
UDC: 
530.182
DOI: 
10.18500/0869-6632-2022-30-3-268-275

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

Autors: 
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
Abstract: 

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.

Key words: 
many-body localization
open quantum systems
neural networks
Acknowledgments: 
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
Reference: 
  1. Bellman RE. Dynamic Programming. Princeton: Princeton University Press; 1957. 365 p.
  2. Meyerov I, Liniov A, Ivanchenko M, Denisov S. Simulating quantum dynamics: Evolution of algorithms in the HPC context. Lobachevskii Journal of Mathematics. 2020;41(8):1509–1520. DOI: 10.1134/S1995080220080120.
  3. Eisert J, Cramer M, Plenio MB. Colloquium: Area laws for the entanglement entropy. Rev. Mod. Phys. 2010;82(1):277–306. DOI: 10.1103/RevModPhys.82.277.
  4. Vidal G. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 2003;91(14):147902. DOI: 10.1103/PhysRevLett.91.147902.
  5. Carleo G, Troyer M. Solving the quantum many-body problem with artificial neural networks. Science. 2017;355(6325):602–606. DOI: 10.1126/science.aag2302.
  6. Levine Y, Sharir O, Cohen N, Shashua A. Quantum entanglement in deep learning architectures. Phys. Rev. Lett. 2019;122(6):065301. DOI: 10.1103/PhysRevLett.122.065301.
  7. Goodfellow I, Bengio Y, Courville A. Deep Learning. Cambridge, Massachusetts: The MIT Press; 2016. 800 p.
  8. Melko RG, Carleo G, Carrasquilla J, Cirac JI. Restricted Boltzmann machines in quantum physics. Nature Physics. 2019;15(9):887–892. DOI: 10.1038/s41567-019-0545-1.
  9. Deng DL, Li X, Das Sarma S. Quantum entanglement in neural network states. Phys. Rev. X. 2017;7(2):021021. DOI: 10.1103/PhysRevX.7.021021.
  10. Lindblad G. On the generators of quantum dynamical semigroups. Commun. Math. Phys. 1976;48(2):119–130. DOI: 10.1007/BF01608499.
  11. Vicentini F, Biella A, Regnault N, Ciuti C. Variational neural-network ansatz for steady states in open quantum systems. Phys. Rev. Lett. 2019;122(25):250503. DOI: 10.1103/PhysRevLett.122.250503.
  12. Hartmann MJ, Carleo G. Neural-network approach to dissipative quantum many-body dynamics. Phys. Rev. Lett. 2019;122(25):250502. DOI: 10.1103/PhysRevLett.122.250502.
  13. Torlai G, Melko RG. Latent space purification via neural density operators. Phys. Rev. Lett. 2018;120(24):240503. DOI: 10.1103/PhysRevLett.120.240503.
  14. Yoshioka N, Hamazaki R. Constructing neural stationary states for open quantum many-body systems. Phys. Rev. B. 2019;99(21):214306. DOI: 10.1103/PhysRevB.99.214306.
  15. Vakulchyk I, Yusipov I, Ivanchenko M, Flach S, Denisov S. Signatures of many-body localization in steady states of open quantum systems. Phys. Rev. B. 2018;98(2):020202. DOI: 10.1103/PhysRevB.98.020202.
  16. Pal A, Huse DA. Many-body localization phase transition. Phys. Rev. B. 2010;82(17):174411. DOI: 10.1103/PhysRevB.82.174411.
  17. Becca F, Sorella S. Quantum Monte Carlo Approaches for Correlated Systems. Cambridge: Cambridge University Press; 2017. 274 p. DOI: 10.1017/9781316417041.
  18. NetKet [Electronic resource]. Available from: https://www.netket.org.
Received: 
28.10.2021
Accepted: 
23.12.2021
Published: 
31.05.2022
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