Exact diagonalization of the Hubbard model on graphics processing units

Topi Siro, Ari Harju
Aalto University School of Science, P.O. Box 14100, 00076 Aalto, Finland
arXiv:1204.3425v1 [physics.comp-ph] (16 Apr 2012)


   author={Siro}, T. and {Harju}, A.},

   title={"{Exact diagonalization of the Hubbard model on graphics processing units}"},

   journal={ArXiv e-prints},




   keywords={Physics – Computational Physics, Condensed Matter – Strongly Correlated Electrons},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a one-dimensional ring and a two-dimensional square lattice. In the one-dimensional case, we obtain speedups of over 100 and 60 in single and double precision arithmetic, respectively. In the two-dimensional case, the corresponding speedups are over 110 and 70.
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