Universal behavior of a bipartite fidelity at quantum criticality

TL;DR

This paper introduces the bipartite fidelity as a measure of ground-state overlap in quantum systems, revealing universal scaling at criticality and potential for identifying phase transitions and central charge.

Contribution

It establishes the universal logarithmic scaling of bipartite fidelity at 1D quantum critical points and explores its properties analogous to entanglement entropy.

Findings

Bipartite fidelity scales as ln(ell) at 1D quantum critical points.

The prefactor of the scaling relates to the central charge c.

It can be used to locate quantum phase transitions and determine the central charge.

Abstract

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. We also argue that this quantity can be useful to locate 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.