Implementation of the SU(2) Hamiltonian Symmetry for the DMRG Algorithm

TL;DR

This paper extends the DMRG++ code to incorporate non-local SU(2) symmetry, enhancing computational efficiency for Hubbard models relevant to superconductors by exploiting symmetry-based matrix blocking and parallelization.

Contribution

The paper introduces a model-independent implementation of SU(2) symmetry in DMRG, improving efficiency and addressing computational bottlenecks with parallelization techniques.

Findings

Significant CPU time reductions observed in Hubbard model simulations.

Effective handling of non-local SU(2) symmetry in DMRG++ code.

Enhanced parallelization improves computational performance.

Abstract

In the Density Matrix Renormalization Group (DMRG) algorithm, Hamiltonian symmetries play an important role. 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 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.