We study the low-temperature phase diagram of quantum Kitaev-Heisenberg spin-orbital models with XXZ anisotropy on the honeycomb lattice. Within a parton mean-field theory, we identify three different quantum phases, distinguished by their symmetries. Besides a disordered spin-orbital liquid with unbroken $\mathrm{U}\left(1\right)\times {\mathbb{Z}}_2$ spin rotational symmetry, there are two orbital liquid phases characterized by spin long-range order. In these phases, the spin rotational symmetry is spontaneously broken down to residual U(1) and ${\mathbb{Z}}_2$ symmetries, respectively. The symmetric spin-orbital liquid features three flavors of linearly dispersing gapless Majorana fermions. In the symmetry-broken phases, one of the three Majorana excitations remains gapless, while the other two acquire a band gap. The transitions from the symmetric to the symmetry-broken phases are continuous and fall into the fractionalized Gross-Neveu-${\mathbb{Z}}_2^{*}$ and Gross-Neveu-SO(2)${}^{*}$ universality classes, respectively. The transition between the ordered phases is discontinuous. Using a renormalization group analysis based on the epsilon expansion, we demonstrate that the triple point in the phase diagram features fractionalized fermionic multicriticality with emergent SO(3) symmetry.

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• Frustrated magnetism
• Quantum criticality
• Quantum spin liquid
• Strongly correlated systems
• Gross-Neveu model
• Kitaev model
• Renormalization group