Polynomially filtered exact diagonalization approach to many-body localization

TL;DR

The paper introduces POLFED, a polynomially filtered exact diagonalization method that efficiently finds eigenstates near a target energy in large sparse matrices, demonstrated on many-body localization in quantum spin chains.

Contribution

A novel polynomial filtering approach (POLFED) for large sparse matrices that improves memory efficiency over existing methods and is applied to study many-body localization.

Findings

POLFED effectively analyzes many-body localization transition.

Finite-size effects significantly influence entanglement entropy and gap ratio.

Estimated critical disorder strength for localization transition.

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.