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arXiv · 2005.09534

Polynomially filtered exact diagonalization approach to many-body localization

Piotr Sierant·Maciej Lewenstein·Jakub Zakrzewski
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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 in the system. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.

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cond-mat.dis-nncond-mat.stat-mechcond-mat.str-elquant-ph

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Piotr Sierant, Maciej Lewenstein, Jakub Zakrzewski. 2020-05-19. Polynomially filtered exact diagonalization approach to many-body localization. https://doi.org/10.1103/physrevlett.125.156601

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