arXiv:1110.2032 · Journal of Statistical Mechanics Theory and Experiment

Correlation functions and the boundary qKZ equation in a fractured XXZ chain

Robert Weston

Published Dec 7, 2011• 14 citations

Abstract

We consider correlation functions of the form , where |vac⟩ is the vacuum eigenstate of an infinite antiferromagnetic XXZ chain, |vac⟩′ is the vacuum eigenstate of an infinite XXZ chain which is split in two, and is a local operator. The Hamiltonian of the split chain has no coupling between sites 1 and 0 and has a staggered magnetic field at these two sites; it arises from a tensor product of left and right boundary transfer matrices. We find a simple, exact expression for ⟨vac|vac⟩′ and an exact integral expression for general using the vertex operator approach. We compute the integral when and find a conjectural expression that is analogous to the known formula for the XXZ spontaneous magnetization and reduces to it when the magnetic field is zero. We show that correlation functions obey a boundary qKZ equation of a different level to the infinite XXZ chain with one boundary.

DOI: 10.1088/1742-5468/2011/12/p12002

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