The bipartite fidelity was introduced in 2011 by Stéphan and Dubail as an entanglement measure in quantum many-body systems. It is expressed in terms of the overlap between the groundstate of the whole system and a tensor product of groundstates for two complementary subsystems. For one-dimensional quantum critical systems, the bipartite fidelity has an interpretation in terms of conformal field theory (CFT), and its asymptotic behavior depends on the conformal data of the underlying CFT.
I will discuss the bipartite fidelity for the XXZ spin chain at $\Delta=-1/2$. The combinatorial structure of the model allows us to derive exact finite-size expressions for the overlaps, and to investigate their asymptotic behavior. In particular, our results agree with the CFT predictions of Stéphan and Dubail. This talk is based on arXiv:2111.15223, in collaboration with Christian Hagendorf.