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

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 paid central states, which are exponentially close each other in terms system size. We propose a Delta-Davidson (DELDAV) method effciently find interior (including central) many-spin The DELDAV utilizes Delta filter Chebyshev polynomial expansion combined with subspace diagonalization overcome nearly degenerate problem. Numerical experiments on Ising spin chain and glass shards show correctness, effciency, robustness proposed finding well ground states. sought may be employed identify localization phase, chaos, extremely long-time dynamical structure.