Polynomially filtered exact diagonalization approach to many-body localization

• URL: http://arxiv.org/abs/2005.09534v2
• Date: Wed, 16 Sep 2020 12:06:42 GMT
• Title: Polynomially filtered exact diagonalization approach to many-body localization
• Authors: Piotr Sierant, Maciej Lewenstein, Jakub Zakrzewski
• Abstract summary: Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The potential of POLFED is demonstrated examining many-body scaling transition in 1D interacting quantum spin-1/2 chains.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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