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

• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（3）
• 所属期刊栏目: GENERAL
• 页码范围: 157-168
• 页数: 12页
• 语种: 英文
• DOI: 10.1088/1674-1056/abd74a

摘要

Many numerical methods,such as tensor network approaches including density matrix renormalization group calcula-tions,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 cor-rectness,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.