Finite temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals

TL;DR

This paper investigates the finite temperature behavior of metals near an Ising-nematic quantum critical point in two dimensions, revealing a temperature-dependent dynamical critical exponent that differs from the zero-temperature case.

Contribution

It introduces a simple Eliashberg-type approach to analyze the change in dynamical critical exponent from $z=3$ at zero temperature to $z=2$ at finite temperature near the quantum critical point.

Findings

At finite temperature, order parameter fluctuations exhibit $z=2$ dynamics.

The boson self-energy is proportional to $rac{ ext{Omega}}{ ext{gamma}(T)}$, with $ ext{gamma}(T)$ being the temperature-dependent fermion scattering rate.

Results align with recent Monte Carlo simulations showing $z=2$ behavior at finite temperature.

Abstract

We study finite temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent $z=2$, in contrast to $z=3$ found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to $\Omega/\gamma(T)$ at small momenta, where $\gamma(T)$ is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte-Carlo simulations at finite temperature, where results consistent with $z=2$ were found.