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

Abstract

We parallelize the density-matrix renormalization group method to directly extend it to two-dimensional ( n -leg) quantum lattice models. The parallelization is performed mainly on the diagonalization for the superblock Hamiltonian since this step requires enormous memory space as the leg number n increases. The superblock Hamiltonian is divided into three parts, and the corresponding superblock vectors are transformed into matrices whose elements are uniformly distributed into processors. Parallel efficiency increases as the number of states kept, m , increases, and the obtained ground-state energy rapidly converges within a few sweeps. Furthermore, the present algorithm applied to doped 4-leg Hubbard ladders reaches their ground states, which satisfy the Lieb–Mattis theorem with m much smaller than those used in different indirect algorithms.