Destabilization of U(1) Dirac spin-liquids on two dimensional non-bipartite lattices by quenched disorder

Abstract: The stability of the Dirac spin-liquid on two-dimensional lattices has long been debated. It was recently demonstrated [Nature Commun. 10, 4254 (2019) and Phys. Rev. B 93, 144411 (2016)] that the staggered $\pi$-flux Dirac spin-liquid phase on the non-bipartite triangular lattice may be stable in the clean limit. However, quenched disorder plays a crucial role in determining whether such a phase is experimentally viable. For SU(2) spin systems, the effective zero-temperature, low-energy description of Dirac spin-liquids in $(2+1)$ dimensions is given by the compact quantum electrodynamics ($\rm cQED_{2+1}$) which admits monopoles. It is already known that generic quenched random perturbations to the non-compact version of $\rm QED_{2+1}$ (where monopoles are absent) lead to strong-coupling instabilities. In this paper we study $\rm cQED_{2+1}$ in the presence of a class of time-reversal invariant quenched disorder perturbations. We show that in this model, random non-Abelian vector potentials make the symmetry-allowed monopole operators more relevant. The disorder-induced underscreening of monopoles, thus, generically makes the gapless spin-liquid phase fragile.