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

TL;DR

This paper extends the density-matrix renormalization group method to two-dimensional quantum lattice systems using parallel algorithms, improving accuracy and efficiency for large systems.

Contribution

It introduces a parallelization approach for DMRG tailored to 2D systems, enabling handling of larger models with better performance.

Findings

High parallel efficiency with increased states kept

Faster eigenvalue convergence compared to multichain algorithm

Effective handling of large superblock Hamiltonians

Abstract

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.