Density Matrix Renormalisation Group Variants for Spin Systems

TL;DR

This thesis extends the Density Matrix Renormalisation Group (DMRG) method to two-dimensional spin systems and combines it with Green Function Monte Carlo, revealing an intermediate phase with inhomogeneities in frustrated Heisenberg models.

Contribution

It introduces a novel combination of DMRG with GFMC and Stochastic Reconfiguration for 2D spin systems, providing new insights into their phase structure.

Findings

Identification of an intermediate phase with spatial inhomogeneities

Demonstration of good quality results for 2D systems via finite-size scaling

Observation of plaquette formation tendencies in the phase diagram

Abstract

This thesis gives an extension for the Density Matrix Renormalisation Group (DMRG) to two dimensions and described a newly developed combination of the DMRG and a Green Function Monte Carlo simulation (GFMC). The first two chapters focus on the DMRG method. The properties are reviewed and it is shown that good quality results can be obtained for two-dimensional systems through finite-size scaling. In the third and fourth chapter the properties of the two-dimensional frustrated Heisenberg model are analysed using a similar combination of DMRG and finite-size scaling. The final chapter presents the combination of the DMRG and GFMC with Stochastic Reconfiguration (Sorella, Capriotti cond-mat/9902211) We find an intermediate phase between Neel and collinear long-range order. This phase shows spatial inhomogeneities with a tendency towards plaquette formation.