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

• 作 者: Haoyu Guan Wenxian Zhang
• 机 构: School of Physics and Technology,Wuhan University,Wuhan 430072,China
• 出 处: 中国物理B（英文版）
• 发表日期: 2021年3期
• 关键词: numerical exact method interior eigenvalue delta function filter subspace diagon

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.