Exact and scaling form of the bipartite fidelity of the infinite XXZ chain

We find an exact expression for the bipartite fidelity f = |(vac|vac)'|2, where |vac) is the vacuum eigenstate of an infinite-size antiferromagnetic XXZ chain and |vac)' is the vacuum eigenstate of an infinite-size XXZ chain which is split in two. We consider the quantity − ln(f) which has been put forward as a measure of quantum entanglement, and show that the large correlation length ξ behaviour is consistent with a general conjecture -ln (f) ∼ (c)/8 ln (ξ), where c is the central charge of the UV conformal field theory (with c = 1 for the XXZ chain). This behaviour is a natural extension of the existing conformal field theory prediction of -ln(f) ∼ (c)/8 ln(L) for a length L bipartite system with 0<<L<<ξ. (letter)