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

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.

revised version, includes discussion of vertex corrections

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• Non-Fermi liquid at the FFLO quantum critical point
• Free energy and specific heat near a quantum critical point of a metal
• The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study
• Critical behavior of itinerant fermions - role of finite size effects
• Generalized Hertz action and quantum criticality of two-dimensional Fermi systems
• Spin pumping effect in non-Fermi liquid metals
• Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective