Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

Abstract

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance between the two may lead to charged quantum critical points at which z=1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D=3-ε. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.

RevTex, 4 pages, 1 ps figure

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