Ground state projection of quantum spin systems in the valence bond basis

TL;DR

This paper introduces a Monte Carlo method using valence bond basis states to efficiently project and analyze the ground state of quantum spin systems, overcoming sign problems and enabling new insights into resonating valence-bond physics.

Contribution

The paper develops a novel Monte Carlo approach in the valence bond basis that improves ground state projection and extends the study of quantum spin models without sign issues.

Findings

Successfully computed the valence bond distribution in the 2D Heisenberg antiferromagnet ground state.

Provides an improved estimator for the singlet-triplet gap.

Demonstrates extension to fermion systems.

Abstract

A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations of the method to fermion systems are also discussed.