Perturbative non-Fermi liquids from dimensional regularization

TL;DR

This paper introduces a dimensional regularization approach to study non-Fermi liquid states in quantum field theories with Fermi surfaces, providing a controlled expansion near the critical dimension and analyzing the Ising-nematic quantum critical point.

Contribution

It develops a novel dimensional regularization scheme for Fermi surface theories and applies it to analyze non-Fermi liquids near the critical dimension, including two-loop critical exponent calculations.

Findings

Identifies the critical dimension as d_c=5/2 for Fermi surface coupled to a critical boson.

Shows the Ising-nematic critical point is a stable non-Fermi liquid state below the critical dimension.

Calculates critical exponents up to two-loop order for the non-Fermi liquid state.

Abstract

We devise a dimensional regularization scheme for quantum field theories with Fermi surface to study scaling behaviour of non-Fermi liquid states in a controlled approximation. Starting from a Fermi surface in two space dimensions, the co-dimension of Fermi surface is extended to a general value while the dimension of Fermi surface is fixed. When Fermi surface is coupled with a critical boson centered at zero momentum, the interaction becomes marginal at a critical space dimension d_c=5/2. A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of Fermi surface is coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed upto the two-loop order.