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It is known that the statistical properties of the spectrum provide anessential characterization of quantum chaos. The computation of a large groupof interior eigenvalues at the middle spectrum is thus an important problem forquantum many-body systems. We propose a dual application of Chebyshevpolynomial (DACP) method to effciently find thousands of central eigenvalues,which are exponentially close to each other in terms of the system size. Tocope with the near-degenerate problem, we use the Chebyshev polynomial to bothconstruct an exponential of semicircle filter as the preconditioning step andgenerate a large set of proper states as the basis of the desired subspace.Besides, DACP owes an excellent property that its computation time is notinfluenced by the required number of eigenvalues. Numerical experiments onIsing spin chain and spin glass shards show the correctness and effciency ofthe proposed method. As our results demonstrate, DACP is a factor of 30 fasterthan the state-of-the-art shift-invert method for the Ising spin chain while 8times faster for the spin glass shards. The memory requirements scale betterwith system size and could be a factor of 100 less than in the shift-invertapproach.

Dual application of Chebyshev polynomial for efficiently computing thousands of central eigenvalues in many-spin systems