Universal behavior of a bipartite fidelity at quantum criticality

We introduce the (logarithmic) bipartite fidelity of a quantum system A boolean OR B as the (logarithm of the) overlap between its ground state wavefunction and the ground state that one would obtain if the interactions between two complementary subsystems A and B were switched off. We argue that it should typically satisfy an area law in dimension d > 1. In the case of one-dimensional quantum critical points (QCP) we find that it admits a universal scaling form, similar to ln l, where l is the typical size of the smaller subsystem. The prefactor is proportional to the central charge c and depends on the geometry. We also argue that this quantity can be useful for locating quantum phase transitions, allows for a reliable determination of the central charge, and in general exhibits various properties that are similar to the entanglement entropy. Like the entanglement entropy, it contains subleading universal terms in the case of a 2D conformal QCP.