Scale perturbation in valence bond ground states

TL;DR

This paper introduces a new method combining valence bond structures and real space renormalization to efficiently compute ground states of antiferromagnetic systems, revealing insights into topological order and quantum communication.

Contribution

It presents a novel approach that unifies valence bond theory with real space renormalization to analyze the Haldane phase in spin-1 chains.

Findings

Describes the entire Haldane phase from AKLT to Heisenberg models.

Links topological order to potential quantum communication applications.

Provides a unified framework for ground state calculations in antiferromagnets.

Abstract

A simple and efficient method for calculating the ground state for a class of antiferromagnet systems is presented. It combines the valence bond structure of the ground state for this class of systems and real space renormalization group. As an example, the entire Haldane phase for a spin-1 chain is described, from the AKLT model through to the Heisenberg model, ending at the critical WZNW $SU_2(2)$ model. The picture that emerges from this new method leads us to consider the relationship between the hidden topological order that characterizes the Haldane phase and potential applications in quantum communication technology.