# Non-Fermi liquids at finite temperature: normal state and infrared singularities

## TL;DR

This paper investigates finite-temperature effects on non-Fermi liquids with massless bosons, revealing new infrared singularities and a novel thermal non-Fermi liquid regime that influences quantum criticality, superconductivity, and transport.

## Contribution

It introduces a non-perturbative resolution to infrared divergences at finite temperature, defining a new thermal non-Fermi liquid regime absent at zero temperature.

## Key findings

- Identification of infrared singularities at finite temperature.
- Development of a non-perturbative approach to resolve divergences.
- Discovery of a wide-ranging thermal non-Fermi liquid regime.

## Abstract

We analyze quantum criticality at finite temperature for a class of non-Fermi liquids with massless bosons. Finite temperature gives rise to new infrared singularities that invalidate standard perturbative treatments. We show how such divergences are resolved at a non-perturbative level, and obtain the resulting fermion self-energy. This leads to a new "thermal" non-Fermi liquid regime that extends over a wide range of frequencies, and which is absent from the zero temperature critical point. We analyze the resulting quantum critical region and properties of the retarded Green's function. More generally, such effects dominate in the nearly static limit and are expected to have a nontrivial impact on superconductivity and transport.