Real-Space Parallel Density Matrix Renormalization Group

TL;DR

This paper introduces a parallelized version of the real-space DMRG algorithm, significantly enhancing computational efficiency for complex two-dimensional quantum systems and large parameter studies.

Contribution

It presents a straightforward modification to serial DMRG enabling efficient parallelization, expanding the scope of feasible simulations in quantum many-body physics.

Findings

Achieved at least tenfold speedup in DMRG computations

Successfully applied parallel DMRG to study valence-bond-solid order

Validated the approach with benchmark results on lattice models

Abstract

We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at least an order of magnitude more computational power to challenging simulations, greatly accelerating investigations of two-dimensional systems and large parameter spaces. We discuss details of the algorithm and present benchmark results including a study of valence-bond-solid order within the square-lattice Q2 model and Neel order within the triangular lattice Heisenberg model. The parallel DMRG algorithm also motivates an alternative canonical form for matrix product states.