title: Universal behavior of the Shannon mutual information of critical quantum chains.
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 study 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.
authors.affiliation: Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil.
authors.forename: F C
authors.initials: FC
authors.lastname: Alcaraz
authors.forename: M A
authors.initials: MA
authors.lastname: Rajabpour