Universal behavior of the Shannon mutual information of critical quantum chains

TL;DR

This paper demonstrates that the Shannon mutual information in critical quantum chains exhibits universal behavior related to the conformal anomaly, allowing identification of universality classes from finite-size data.

Contribution

It analytically and numerically shows the universal finite-size behavior of Shannon mutual information in various critical quantum chains, linking it to conformal field theory parameters.

Findings

Shannon mutual information reveals the conformal anomaly c.

Finite-size behavior detects universality class.

Results apply to multiple quantum chain models.

Abstract

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly $c$ of the underlying conformal field theory governing the long distance physics of the quantum chain. We studied analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models ($Q = 2$; 3 and 4), the XXZ quantum chain and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes its finite-size behavior already detects the universality class of quantum critical behavior.