On the stability of U(1) spin liquids in two dimensions

TL;DR

The paper addresses whether 2D spin liquids with gapless Dirac spinons coupled to a fluctuating $U(1)$ gauge field can remain deconfined, by embedding the problem in an SU($N$) generalization and analyzing the large-$N$ limit of compact QED$_3$ with $2N$ Dirac flavors. Through a combination of operator analysis constrained by the projective symmetry group and an approximate renormalization group treatment, the authors show that monopole fluctuations are irrelevant and no perturbations destabilize the large-$N fixed point, yielding a stable deconfined phase for large $N$. A key result is the coupled RG flow with $\frac{\partial z}{\partial \ell} = \left(3 - \frac{g \Lambda}{\pi}\right) z$ and $\frac{\partial g}{\partial \ell} = -g - \frac{c g^3 z^2}{\Lambda^4} + \frac{\pi \eta N}{\Lambda}$, which yields a fixed point $g^* = \frac{\pi \eta N}{\Lambda}$ and $z \to 0$ when $N\eta > 3$, signaling deconfinement. The work critiques the monopole-screening argument and demonstrates that, at large $N$, the π-flux spin liquid is a stable, deconfined critical phase with an emergent topological $U(1)$ symmetry; however, extending these results to physical $SU(2)$ spins remains an open challenge.

Abstract

We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless U(1) gauge fluctuations can be stable in two dimensions, at least when the physical SU(2) spin symmetry is generalized to SU(N). Equivalently, we show that compact QED3 has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological U(1) symmetry corresponding to the conservation of gauge flux. Beginning with an SU(N) generalization of the S=1/2 square lattice Heisenberg antiferromagnet, we consider the pi-flux spin liquid and, via a systematic analysis of all operators, show that there are NO relevant perturbations (in the renormalization group sense) about the large-N spin liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous "screening" argument for the relevance of monopoles in compact QED3.