Fractionalized Fermionic Quantum Criticality in Spin-Orbital Mott Insulators

We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu* universality classes in ($2+1$) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t\text{−}V$ model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ $\epsilon$-expansion and large-$N$ methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with $d^1$ electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.

Figure 1

(a) Adding a sufficiently strong antiferromagnetic Ising spin interaction to the ${\nu }_M=2$ Kitaev spin-orbital liquid (SOL) on the square lattice gives rise to Ising antiferromagnetic order in the spin sector, with the remaining degrees of freedom described in terms of a ${\mathbb{Z}}_2$ gauge theory. The continuous transition at $J_{\mathrm{c}}^z/K=0.641(2)$ is in the Gross-Neveu-${{\mathbb{Z}}_2}^{*}$ universality class. (b) The honeycomb-lattice model features a Gross-Neveu-${\text{SO}(3)}^{*}$ quantum critical point at $J_{\mathrm{c}}/K=0.9(2)$ between the ${\nu }_M=3$ Kitaev SOL and a ${\nu }_M=1$ Kitaev SOL with Néel order in the spin sector.

Figure 2

The Néel spin-order parameter (black dots) and the ground-state expectation value of the plaquette operator $W_p^{(3)}$ (blue triangles) as a function of $J/K$ in the spin-orbital model ${\mathcal{H}}^{(3)}$ from iDMRG calculations performed on an infinite cylinder with circumference of $L_y=4$ unit cells. The iDMRG uses two unit cells along the $x$ direction as its translationally invariant building block and the bond dimension is $\chi =1000$.