Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions

TL;DR

This paper investigates the critical behavior of dephasing rates near metal-insulator and quantum Hall transitions, combining analytical and numerical methods to understand interaction effects on phase coherence.

Contribution

It provides a combined analytical and numerical analysis of dephasing near quantum critical points, including identification of operators and renormalization-group analysis in $2+ ext{epsilon}$ dimensions.

Findings

Critical dephasing exponent characterized near Anderson transitions.

Analytical identification of operators responsible for dephasing.

Numerical simulations support the analytical scaling analysis.

Abstract

We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in $2+\epsilon$ dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.