Universal behavior of a bipartite fidelity at quantum criticality

Understand

We introduce the (logarithmic) bipartite fidelity of a quantum system $A\cup B$ as the (logarithm of the) overlap between its ground-state wave function and the ground-state 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 $\sim \ln \ell$, where $\ell$ is the typical size of the smaller subsystem.
• The prefactor is proportional to the central charge $c$ and depends on the geometry.