  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.
