Polynomially Filtered Exact Diagonalization Approach to Many-Body Localization

Piotr Sierant, Maciej Lewenstein, and Jakub Zakrzewski
Phys. Rev. Lett. 125, 156601 – Published 9 October 2020
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Abstract

Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale better with system size than in the state-of-the-art shift-invert approach. The potential of POLFED is demonstrated examining many-body localization transition in 1D interacting quantum spin-1/2 chains. We investigate the disorder strength and system size scaling of Thouless time. System size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.

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  • Received 27 May 2020
  • Accepted 13 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.156601

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Piotr Sierant1,2,*, Maciej Lewenstein2,3,†, and Jakub Zakrzewski1,4,‡

  • 1Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
  • 2ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
  • 3ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
  • 4Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland

  • *piotr.sierant@uj.edu.pl
  • maciej.lewenstein@icfo.eu
  • jakub.zakrzewski@uj.edu.pl

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Issue

Vol. 125, Iss. 15 — 9 October 2020

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