Direct Extension of Density-Matrix Renormalization Group toward 2-Dimensional Quantum Lattice Systems: Studies for Parallel Algorithm, Accuracy, and Performance

Details Direct Extension of Density-Matrix Renormalization Group toward 2-Dimensional Quantum Lattice Systems: Studies for Parallel Algorithm, Accuracy, and Performance Direct Extension of Density-Matrix Renormalization Group toward 2-Dimensional Quantum Lattice Systems: Studies for Parallel Algorithm, Accuracy, and Performance

2007-07-02

arxiv.org/abs/0707.0159v1

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

We parallelize density-matrix renormalization group to directly extend it to 2-dimensional ($n$-leg) quantum lattice models. The parallelization is made mainly on the exact diagonalization for the superblock Hamiltonian since the part requires an enormous memory space as the leg number $n$ increases. The superblock Hamiltonian is divided into three parts, and the correspondent superblock vector is transformed into a matrix, whose elements are uniformly distributed into processors. The parallel efficiency shows a high rate as the number of the states kept $m$ increases, and the eigenvalue converges within only a few sweeps in contrast to the multichain algorithm.

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