Time dynamics with matrix product states: Many-body localization transition of large systems revisited

Titas Chanda, Piotr Sierant, and Jakub Zakrzewski
Phys. Rev. B 101, 035148 – Published 29 January 2020

Abstract

We compare the accuracy of two prime time evolution algorithms involving matrix product states—tDMRG (time-dependent density matrix renormalization group) and TDVP (time-dependent variational principle). The latter is supposed to be superior within a limited and fixed auxiliary space dimension. Surprisingly, we find that the performance of algorithms depends on the model considered. In particular, many-body localized systems as well as the crossover regions between localized and delocalized phases are better described by tDMRG, contrary to the delocalized regime where TDVP indeed outperforms tDMRG in terms of accuracy and reliability. As an example, we study many-body localization transition in a large size Heisenberg chain. We discuss drawbacks of previous estimates [Phys. Rev. B 98, 174202 (2018)] of the critical disorder strength for large systems.

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  • Received 23 August 2019
  • Revised 27 November 2019

DOI:https://doi.org/10.1103/PhysRevB.101.035148

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Titas Chanda1, Piotr Sierant1,*, and Jakub Zakrzewski1,2

  • 1Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland
  • 2Mark Kac Complex Systems Research Center, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland

  • *piotr.sierant@uj.edu.pl

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Vol. 101, Iss. 3 — 15 January 2020

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