Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
May, 2011
4 pages
Published in:
- Phys.Rev.E 84 (2011) 056701
e-Print:
- 1105.0007 [cond-mat.str-el]
Report number:
- SLAC-PUB-14373
Citations per year
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 is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of smaller subcluster vectors using singular value decomposition. For low entanglement entropy , (satisfied by short range Hamiltonians), the truncation error is expected to vanish as . 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.- 05.50.+q
- 02.70.-c
- 03.67.Mn
- 05.30.-d
References(15)
Figures(8)