Can Density-matrix renormalization group be Applied to two dimensional systems?

TL;DR

This paper explores extending the DMRG method to two-dimensional systems by developing new initial state preparation techniques and analyzing the growth of required states, demonstrating the method's variational properties.

Contribution

The paper introduces two alternative methods for initial state preparation in 2D DMRG and analyzes the growth of states needed for accuracy, advancing the application of DMRG to 2D systems.

Findings

Number of states needed grows exponentially with system size

States in DMRG preserve Hamiltonians for high accuracy

Finite cluster energy is a variational upper bound

Abstract

In order to extend the density-matrix renormalization-group (DMRG) method to two-dimensional systems, we formulate two alternative methods to prepare the initial states. We find that the number of states that is needed for accurate energy calculations grows exponentially with the linear system size. We also analyze how the states kept in the DMRG method manage to preserve both the intrablock and interblock Hamiltonians, which is the key to the high accuracy of the method. We also prove that the energy calculated on a finite cluster is always a variational upper bound.