Critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals

TL;DR

This paper analytically investigates the critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals, revealing a sizable fluctuation regime above the transition.

Contribution

It provides explicit analytic expressions for $T_c$ and $T_{ m G}$ near a quantum critical point using renormalization group analysis of the Hertz action.

Findings

Ginzburg regime occupies a significant part of the phase diagram.

Logarithmic corrections are included in the expressions for $T_c$ and $T_{ m G}$.

The analysis is based on a scalar order parameter in a 2D metallic system.

Abstract

We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{\rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for $T_c$ and $T_{\rm G}$ as a function of the non-thermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between $T_c$ and $T_{\rm G}$ occupies a sizable part of the phase diagram.