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

TL;DR

This paper demonstrates that U(1) spin liquids with gapless fermionic spinons can be stable in two dimensions when generalized to SU(N), showing that monopole fluctuations become irrelevant at low energies for large N.

Contribution

The study proves the stability of gapless U(1) spin liquids in 2D for large N by analyzing monopole irrelevance and operator relevance, extending the understanding of quantum spin liquids.

Findings

U(1) spin liquids are stable in 2D for large N.

Monopole fluctuations are irrelevant at low energies.

Large-N analysis shows no relevant perturbations at the fixed point.

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.