On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta=-1/2$

TL;DR

This paper derives an exact finite-size formula for the logarithmic bipartite fidelity of the open XXZ spin chain at .5 anisotropy, confirming conformal field theory predictions through asymptotic analysis.

Contribution

It provides a determinant formula for ground-state overlaps at different lengths, enabling precise calculation of the fidelity in the open XXZ chain at .5.

Findings

Exact finite-size formula for bipartite fidelity

Asymptotic terms match conformal field theory predictions

Determinant expression for ground-state overlaps

Abstract

The open XXZ spin chain with the anisotropy $\Delta=-\frac12$ and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain's ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state's logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.