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-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.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-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.

May 28, 20010 citations

Conductivity near quantum criticality in two space dimensions

Snir Gazit, Daniel K. Podolsky, Assa Auerbach +1 more

Bulletin of the American Physical SocietyMar 3, 20140 citations

Quantum Critical Points with the Coulomb Interaction and the Dynamical Exponent: When and Why z=1

Igor F. Herbut

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on $z$ , and that balance between the two may lead to charged quantum critical points at which $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\ensuremath{\epsilon}$. Precisely in $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ , however, the above simple result breaks down, and $z>1$ . Relation to other studies is discussed.A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on $z$, and that balance between the two may lead to charged quantum critical points at which $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\ensuremath{\epsilon}$. Precisely in $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, however, the above simple result breaks down, and $z>1$. Relation to other studies is discussed.

arXiv:cond-mat/0105544Physical Review LettersSep 10, 200162 citations

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent

z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on

z

, and that balance between the two may lead to charged quantum critical points at which

z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\ensuremath{\epsilon}$. Precisely in

D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3

, however, the above simple result breaks down, and

z>1

. Relation to other studies is discussed.