Polynomially Filtered Exact Diagonalization Approach to Many-Body Localization
Oct 9, 2020Published in:
- Phys.Rev.Lett. 125 (2020) 15, 156601
- Published: Oct 9, 2020
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Abstract: (APS)
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- 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.References(120)
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