A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm

TL;DR

This paper introduces a novel two-dimensional infinite system DMRG algorithm that enables direct calculations in 2D, allowing the study of fixed points and demonstrating potential for large-scale 2D system analysis.

Contribution

The paper presents a new 2D infinite system DMRG algorithm that directly addresses the challenges of extending DMRG to large 2D systems.

Findings

Existence of an algorithm with monotonically decreasing local energy

Potential feasibility of large 2D system analysis using this method

First study of fixed points in two-dimensional systems

Abstract

It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it possible to use an infinite system method, and for the first time the fixed point in two dimensions is studied. By analyzing several related blocking schemes I find that there exists an algorithm for which the local energy decreases monotonically as the system size increases, thereby showing the potential feasibility of this method.