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

The stability of the Dirac spin liquid on two-dimensional lattices has long been debated. It was recently demonstrated [Nat. Commun. 10, 4254 (2019) and Phys. Rev. B 93, 144411 (2016)] that the staggered $\pi$-flux Dirac spin-liquid phase on the nonbipartite 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 $\left({\mathrm{cQED}}_{2+1}\right)$ which admits monopoles. It is already known that generic quenched random perturbations to the noncompact version of ${\mathrm{QED}}_{2+1}$ (where monopoles are absent) lead to strong-coupling instabilities. In this paper we study ${\mathrm{cQED}}_{2+1}$ 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.

Figure 1

The bare scaling dimension of monopole operators [Eq. (32)] as a function of bare random current strength $\rho$ with $\left(2N\right)=4$ flavors of fermions. The gray line denotes the threshold minimum ${\mathrm{\Delta }}_{{\mathcal{M}}^{\left(q\right)}}=3$, below which the monopoles proliferate. In the triangular lattice staggered $\pi$-flux spin-liquid state which only allows monopole operators of charges $q\ge 3/2$, disorder reduces the scaling dimension of monopoles of all charges.

Figure 2

The combined RG flow of $\mathrm{SU}(N$) symmetric random current coupling ${\rho }_x={\rho }_y={\rho }_z=\tilde{\rho }$ and monopole fugacity $y^{\left(q\right)}$ of the $q=3/2$ monopole operator which is allowed for the triangular lattice staggered $\pi$-flux U(1) Dirac spin-liquid state.

Figure 3

The phase diagram of the U(1) Dirac spin liquid with $2N$ flavors of fermions coupled to RG marginal $\mathrm{U}\left(1\right)\times \mathrm{SU}\left(\mathrm{N}\right)$ symmetric random current perturbations when only the monopole operators with charge $q\ge 3/2$ are symmetry allowed. In the triangular lattice the microscopic lattice symmetries disallow monopoles of charge $q<3/2$ for the staggered $\pi$-flux ansatz. The gray line indicates the case of the triangular lattice staggered $\pi$-flux Dirac spin-liquid state which has $\left(2N\right)=4$.