Sommaire:

We consider correlation functions of the form <vac|O|vac>', 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 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 <vac|O|vac>' using the vertex operator approach. We compute the integral when O = \sigma^z and find a conjectural expression that is analogous to the known formula for the XXZ spontaneous magnetisation and reduces to it when the boundary 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. One application is that the bipartite fidelity f=|<vac|vac>'|^2 provides a measure of quantum entanglement of a bipartite system. The scaling form of -ln(f) is computed and shown to be consistent with a conjectured universal form c/8 log(xi) involving the central charge c and correlation length xi.

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