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arXiv · 1203.2326

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

Robert Weston
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Abstract

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 <<xi.

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Robert Weston. 2012-03-11. Exact and Scaling Form of the Bipartite Fidelity of the Infinite XXZ Chain. https://doi.org/10.1088/1742-5468%2F2012%2F04%2Fl04001

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