Studying Two Dimensional Systems With the Density Matrix Renormalization Group

TL;DR

This paper reviews the application of the Density Matrix Renormalization Group (DMRG) method to two-dimensional systems, highlighting techniques for improving convergence and comparing it with tensor network methods.

Contribution

It introduces advanced techniques for 2D DMRG studies and compares its performance with recent tensor network approaches.

Findings

DMRG remains powerful for 2D systems with sign problems

Techniques for convergence and data extrapolation are presented

Comparison shows current tensor network methods have competitive performance

Abstract

The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past applications of DMRG in 2D demonstrates its success in treating a wide variety of problems, although it remains underutilized in this setting. We present techniques for performing cutting edge 2D DMRG studies including methods for ensuring convergence, extrapolating finite-size data and extracting gaps and excited states. Finally, we compare the current performance of a recently developed tensor network method to 2D DMRG.