Exact and Scaling Form of the Bipartite Fidelity of the Infinite XXZ Chain

Details Exact and Scaling Form of the Bipartite Fidelity of the Infinite XXZ Chain Exact and Scaling Form of the Bipartite Fidelity of the Infinite XXZ Chain

2012-03-11

arxiv.org/abs/1203.2326v1

Physics

Mathematical Physics

6 pages

Scientific paper

We find an exact expression for the bipartite fidelity f=|'|^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 xi behaviour is consistent with a general conjecture -ln(f) ~ c/8 ln(xi), 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 <

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