Quantum critical metals in $4-\epsilon$ dimensions

TL;DR

This paper analyzes a quantum critical metal model in 4−ε dimensions, revealing a complex RG flow with NFL behavior and potential relevance to high-temperature superconductors.

Contribution

It provides a detailed RG analysis of a Fermi surface coupled to a scalar boson in 4−ε dimensions, including backreaction effects and phase diagram insights.

Findings

Fermi velocity flows to zero above Landau damping scale

The theory flows to a z=3 scalar with non-Fermi liquid properties

Fermi velocity and quasiparticle residue vanish as a power-law near the fixed point

Abstract

We study the quantum theory of a Fermi surface coupled to a gapless boson scalar in $D=4-\epsilon$ spacetime dimensions as a simple model for non-Fermi liquids (NFL) near a quantum phase transition. Our analysis takes into account the full backreaction from Landau damping of the boson, and obtains an RG flow that proceeds through three distinct stages. Above the scale of Landau damping the Fermi velocity flows to zero, while the coupling evolves according to its classical dimension. Once damping becomes important, its backreaction leads to a crossover regime where dynamic and static damping effects compete and the fermion self-energy does not respect scaling. Below this crossover and having tuned the boson to criticality, the theory flows to a $z=3$ scalar interacting with a NFL. By increasing the number of bosonic flavors, the phase diagram near the quantum critical point interpolates between a superconducting dome fully covering the NFL behavior, and a phase where NFL effects become important first, before the onset of superconductivity. A generic prediction of the theory is that the Fermi velocity and quasiparticle residue vanish with a power-law $\omega^\epsilon$ as the fixed point is approached. These features may be useful for understanding some of the phenomenology of high $T_c$ materials in a systematic $\epsilon$--expansion.