Valence Bond Mapping of Antiferromagnetic Spin Chains

TL;DR

This paper introduces boson mapping techniques to analyze valence bond correlations in quantum spin chains, providing an analytic method that accurately predicts transition points in antiferromagnetic systems.

Contribution

It develops a novel boson mapping approach for valence bond analysis and derives an analytic expression for transition points in spin chains.

Findings

Analytic expression for transition points matches DMRG and QMC results.

Method effectively describes valence bond correlations in antiferromagnetic chains.

Provides a new tool for studying quantum spin chain phase transitions.

Abstract

Boson mapping techniques are developed to describe valence bond correlations in quantum spin chains. Applying the method to the alternating bond hamiltonian for a generic spin chain, we derive an analytic expression for the transition points which gives perfect agreement with existing Density Matrix Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) calculations.