Two-dimensional confinement of critical U(1) gauge field in the presence of Fermi surface

TL;DR

This paper demonstrates that the U(1) gauge field in two-dimensional systems with a Fermi surface must be confined, challenging the stability of certain quantum spin liquids and fractionalized metallic states described by such gauge fields.

Contribution

It shows that the U(1) gauge field with a positive anomalous dimension is confined in the presence of a Fermi surface, indicating instability of some quantum spin liquids.

Findings

U(1) gauge field is confined with a Fermi surface in 2D

Quantum spin liquids with this gauge field are unstable

New features of fractionalized states near Fermi surface

Abstract

The compact U(1) gauge field occurs in many fractionalized descriptions of low dimensional quantum magnetism and heavy fermion systems. In this respect a fundamental question about the gauge field is whether it is confined or not in the presence of Fermi surface. In this paper we show that the U(1) gauge field with a possible positive anomalous dimension in the presence of Fermi surface has to be in the confined state, although it is strongly coupled to abundant gapless fermionic excitations near the Fermi surface in two spatial dimensions. This means that some quantum spin liquids and/or fractionalized metallic states described in terms of this kind of gauge fields with positive anomalous dimensions are unstable to other possible symmetry-breaking states, as a result, they are not be appropriate candidates for ground states in related systems. The instability obtained shows some novel features of the quantum spin liquids and/or fractionalized metallic states in the presence of Fermi surface which have not been reported in the literature. The result could be useful for further study in the quantum spin liquids and many related slave-particle gauge theories in strongly correlated electron systems.