Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

May, 2011
4 pages
Published in:
  • Phys.Rev.E 84 (2011) 056701
e-Print:
Report number:
  • SLAC-PUB-14373

Citations per year

2013201520172019202110
Abstract: (arXiv)
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size NN is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of nsvdn_{{\rm svd}} smaller subcluster vectors using singular value decomposition. For low entanglement entropy SeeS_{ee}, (satisfied by short range Hamiltonians), the truncation error is expected to vanish as exp(nsvd1/See)\exp(-n_{{\rm svd}}^{1/S_{ee}}). Convergence is tested for the Heisenberg model on Kagom\'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.
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