Renormalization group for phases with broken discrete symmetry near quantum critical points

TL;DR

This paper extends the Hertz-Millis theory to phases with broken discrete symmetry near quantum critical points, using functional renormalization group methods to analyze phase transition lines and fluctuation effects.

Contribution

It introduces a coupled flow equation framework within the functional renormalization group to study quantum phase transitions with broken discrete symmetry.

Findings

Computed the phase transition line T_c(delta) near quantum critical points.

Analyzed the role of quantum and classical fluctuations at different energy scales.

Compared Ginzburg temperature T_G with transition temperature T_c, identifying non-Gaussian fixed points.

Abstract

We extend the Hertz-Millis theory of quantum phase transitions in itinerant electron systems to phases with broken discrete symmetry. Using a set of coupled flow equations derived within the functional renormalization group framework, we compute the second order phase transition line T_c(delta), with delta a non-thermal control parameter, near a quantum critical point. We analyze the interplay and relative importance of quantum and classical fluctuations at different energy scales, and we compare the Ginzburg temperature T_G to the transition temperature T_c, the latter being associated with a non-Gaussian fixed-point.