Deconfinement in the presence of a Fermi surface

TL;DR

This paper investigates the deconfinement of non-relativistic fermions near a Fermi surface within an effective U(1) gauge theory, revealing conditions under which instanton excitations are suppressed and a stable charged fixed point emerges.

Contribution

It demonstrates, through renormalization group analysis, that a stable charged fixed point exists for the U(1) gauge theory with a Fermi surface, extending insights from $QED_3$ to non-relativistic fermions.

Findings

A stable charged fixed point exists for the gauge theory.

Fermion conductivity influences instanton suppression.

A critical non-relativistic fermion gauge theory is identified.

Abstract

U(1) gauge theory of non-relativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions ($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ (the coupling strength between non-relativistic fermions and U(1) gauge fields) reveals that the conductivity $\sigma$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the non-relativistic fermions at the charged fixed point. As a result a critical field theory of non-relativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.