A controlled expansion for certain non-Fermi liquid metals

TL;DR

This paper introduces a new controlled theoretical approach combining 1/N and epsilon expansions to analyze non-Fermi liquid metals, providing systematic calculations of their low energy physics and deviations from RPA results.

Contribution

The authors develop a novel combined expansion method in 1/N and epsilon to systematically study non-Fermi liquids coupled to gapless bosons, applicable to various quantum critical systems.

Findings

Calculated low energy spectra and correlation functions for spin liquids and nematic transitions.

Found deviations from RPA predictions in certain correlation functions.

Demonstrated the method's applicability to quantum spin liquids and Pomeranchuk transitions.

Abstract

The destruction of Fermi liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a new controlled theoretical approach to determining the low energy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter \epsilon = z_b -2 where z_b is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low energy physics of these problems. The method is illustrated by studying spinon fermi surface spin liquids, and a quantum critical metal at a second order electronic nematic phase transition. We calculate the low energy single particle spectra, and various interesting two particle correlation functions. In some cases deviations from the popular Random Phase Approximation results are found. Some of the same universal singularities are also calculated to leading non-vanishing order using a perturbative renormalization group calculation at small N extending previous results of Nayak and Wilczek. Implications for quantum spin liquids, and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition we show that the tunneling density of states has a power law suppression at low energies.