F. C. Alcaraz, M. A. Rajabpour
We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Although this quantity depends on the basis the ground state is expressed our results indicate that its leading behavior is basis independent. 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.
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http://arxiv.org/abs/1305.1239
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