Monte Carlo Renormalization Group Study of the d=1 XXZ Model

TL;DR

This paper presents a Monte Carlo Renormalization Group approach applied to the one-dimensional XXZ quantum spin model, utilizing loop algorithms and symmetry-agnostic methods to study critical phenomena, with preliminary promising results.

Contribution

Introduces a novel MCRG method combining loop algorithms and symmetry-independent renormalization for quantum systems.

Findings

Encouraging preliminary results on the XXZ model

Method reduces critical slowing down

Applicable to models with complex phase transitions

Abstract

We report current progress on the synthesis of methods to alleviate two major difficulties in implementing a Monte Carlo Renormalization Group (MCRG) for quantum systems. In particular, we have utilized the loop-algorithm to reduce critical slowing down, and we have implemented an MCRG method in which the symmetries of the classical equivalent model need not be fully understood, since the Renormalization Group is given by the Monte Carlo simulation. We report preliminary results obtained when the resulting MCRG method is applied to the d=1 XXZ model. Our results are encouraging. However, since this model has a Kosterlitz-Thouless transition, it does not yet provide a full test of our MCRG method.