Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual application of Chebyshev polynomial for efficiently computing
  thousands of central eigenvalues in many-spin systems   It is known that the statistical properties of the spectrum provide an
essential characterization of quantum chaos. The computation of a large group
of interior eigenvalues at the middle spectrum is thus an important problem for
quantum many-body systems. We propose a dual application of Chebyshev
polynomial (DACP) method to effciently find thousands of central eigenvalues,
which are exponentially close to each other in terms of the system size. To
cope with the near-degenerate problem, we use the Chebyshev polynomial to both
construct an exponential of semicircle filter as the preconditioning step and
generate a large set of proper states as the basis of the desired subspace.
Besides, DACP owes an excellent property that its computation time is not
influenced by the required number of eigenvalues. Numerical experiments on
Ising spin chain and spin glass shards show the correctness and effciency of
the proposed method. As our results demonstrate, DACP is a factor of 30 faster
than the state-of-the-art shift-invert method for the Ising spin chain while 8
times faster for the spin glass shards. The memory requirements scale better
with system size and could be a factor of 100 less than in the shift-invert
approach.

22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
18
The categories of this paper are: econ
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph