2020/11/03 by Haoyu Guan, Wenxian Zhang, Guan, Haoyu +1 · 1 citation
Physics and Astronomy · #Computational Physics (physics.comp-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2011.01554
openalex publication_date 2020/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 effciently find such interior (including the central) states in many-spin systems. The DELDAV method utilizes 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, effciency, 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.