Non-Fermi Liquid Behavior In Quantum Critical Systems

TL;DR

This paper investigates how electron gases interacting via transverse gauge bosons exhibit non-Fermi liquid behavior near quantum critical points, revealing exact marginal gauge couplings and specific thermodynamic and transport properties.

Contribution

It demonstrates that the gauge field's long wavelength behavior is Gaussian with a dynamical exponent of 3, leading to non-Fermi liquid behavior in dimensions up to 3.

Findings

Gauge coupling is exactly marginal.

Electron scattering leads to non-Fermi liquid behavior.

Derived asymptotic Green's functions, specific heat, and resistivity.

Abstract

The problem of an electron gas interacting via exchanging transverse gauge bosons is studied using the renormalization group method. The long wavelength behavior of the gauge field is shown to be in the Gaussian universality class with a dynamical exponent $z=3$ in dimensions $D \geq 2$. This implies that the gauge coupling constant is exactly marginal. Scattering of the electrons by the gauge mode leads to non-Fermi liquid behavior in $D \leq 3$. The asymptotic electron and gauge Green's functions, interaction vertex, specific heat and resistivity are presented.