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

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 1and 0 and has a staggered magnetic field at these two sites; it arises from a tensor productof 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 XXZspontaneous magnetization and reduces to it when the magnetic field is zero. We show thatcorrelation functions obey a boundary qKZ equation of a different level to the infinite XXZchain with one boundary.