Implementation of the SU(2) Hamiltonian symmetry for the DMRG algorithm

Gonzalo Alvarez

doi:10.1016/j.cpc.2012.04.025

Implementation of the SU(2) Hamiltonian symmetry for the DMRG algorithm

Gonzalo Alvarez

Computational Chemistry and Nanomaterial

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) [1,2], Hamiltonian symmetries play an important rôle. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) [3] has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and the use of shared memory parallelization are also addressed.

Original language	English
Pages (from-to)	2226-2232
Number of pages	7
Journal	Computer Physics Communications
Volume	183
Issue number	10
DOIs	https://doi.org/10.1016/j.cpc.2012.04.025
State	Published - Oct 2012

Funding

The present code uses part of the psimag toolkit, http://psimag.org/ . I would like to thank Luis G. G. V. Dias da Silva, I. P. McCulloch, M. S. Summers, and J. C. Xavier for helpful discussions. This work was supported by the Center for Nanophase Materials Sciences , sponsored by the Scientific User Facilities Division, Basic Energy Sciences, US Department of Energy, under contract with UT-Battelle, and by the DOE early career research program. This research used resources of the National Center for Computational Sciences, as well as the OIC at Oak Ridge National Laboratory.

Keywords

DMRG
Density-matrix renormalization group
Generic programming
Strongly correlated electrons

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10.1016/j.cpc.2012.04.025

Cite this

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abstract = "In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) [1,2], Hamiltonian symmetries play an important r{\^o}le. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) [3] has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and the use of shared memory parallelization are also addressed.",

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KW - Strongly correlated electrons

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Implementation of the SU(2) Hamiltonian symmetry for the DMRG algorithm

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