Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model

TL;DR

This paper extends the functional renormalization group method to finite temperatures for fermionic systems with broken discrete symmetry, specifically analyzing the charge-density wave mean-field model at half filling, revealing how small initial order grows and saturates.

Contribution

It introduces a finite-temperature fRG scheme for broken discrete symmetries and demonstrates its application to the CDW mean-field model, highlighting differences from continuous symmetry cases.

Findings

Small initial CDW order parameter grows at the instability

Effective interaction peaks and saturates at low energies

Flow suppresses divergence of the effective interaction

Abstract

We generalize the application of the functional renormalization group (fRG) method for the fermionic flow into the symmetry-broken phase to finite temperatures. We apply the scheme to the case of a broken discrete symmetry: the charge-density wave (CDW) mean-field model at half filling. We show how an arbitrarily small initial CDW order parameter starts to grow at the CDW instability and how it flows to the correct final value, suppressing the divergence of the effective interaction in the fRG flow. The effective interaction peaks at the instability and saturates at low energy scales or temperatures. The relation to the mean-field treatment, differences compared to the flow for a broken continuous symmetry, and the prospects of the new method are discussed.