Absence of U(1) spin liquids in two dimensions

TL;DR

This paper demonstrates that in two-dimensional systems, U(1) spin liquids with fermionic spinons on a Fermi surface are unstable due to instanton effects, leading to confinement and the absence of such spin liquids.

Contribution

It generalizes previous confinement results to argue that U(1) spin liquids with Fermi surfaces cannot exist in two dimensions, except when gauge symmetry is broken to a discrete subgroup.

Findings

U(1) spin liquids with Fermi surfaces are unstable in 2D due to instantons.

Elementary excitations in these systems are gauge neutral, preventing spinon Fermi surfaces.

Fractionalized states can exist if gauge symmetry is broken via the Higgs mechanism.

Abstract

Many popular models of fractionalized spin liquids contain neutral fermionic spinon excitations on a Fermi surface, carrying unit charges under a compact U(1) gauge force. We argue that instanton effects generically render such states unstable to confinement in two spatial dimensions, so that all elementary excitations are gauge neutral, and there is no spinon Fermi surface. Similar results are expected to apply to SU(2) spin liquids. However, fractionalized states can appear when the gauge symmetry is broken down to a discrete subgroup by the Higgs mechanism. Our argument generalizes earlier results on confinement in the pure gauge theory, and on the instability of the U(1) staggered flux and algebraic spin liquids with a Dirac spectrum for fermionic spinons.