Correlation Functions and the Boundary qKZ Equation in a Fractured XXZ Chain

Details Correlation Functions and the Boundary qKZ Equation in a Fractured XXZ Chain Correlation Functions and the Boundary qKZ Equation in a Fractured XXZ Chain

2011-10-10

arxiv.org/abs/1110.2032v1

Physics

Mathematical Physics

28 pages, 12 figures

Scientific paper

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 O 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 ' and an exact integral expression for general ' using the vertex operator approach. We compute the integral when O=\sigma^z_1 and find a conjectural expression that is analogous to the known formula for the XXZ spontaneous magnetisation 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.

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