Delta-Davidson method for interior eigenproblem in many-spin systems

doi:10.1088/1674-1056/abd74a

Abstract Many numerical methods, such as tensor network approaches including density matrix renormalization group calculations, have been developed to calculate the extreme/ground states of quantum many-body systems. However, little attention has been paid to the central states, which are exponentially close to each other in terms of system size. We propose a delta-Davidson (DELDAV) method to efficiently find such interior (including the central) states in many-spin systems. The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem. Numerical experiments on Ising spin chain and spin glass shards show the correctness, efficiency, and robustness of the proposed method in finding the interior states as well as the ground states. The sought interior states may be employed to identify many-body localization phase, quantum chaos, and extremely long-time dynamical structure.

Keywords: numerical exact method interior eigenvalue delta function filter subspace diagonalization

Received: 25 August 2020
Revised: 11 December 2020
Accepted manuscript online: 30 December 2020

PACS:

02.70.-c

(Computational techniques; simulations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91836101, U1930201, and 11574239).

Corresponding Authors: ^†Corresponding author. E-mail: wxzhang@whu.edu.cn

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Haoyu Guan(关浩宇) and Wenxian Zhang(张文献) Delta-Davidson method for interior eigenproblem in many-spin systems 2021 Chin. Phys. B 30 030205

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