Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain

Abstract: Higher-spin quantum magnets with competing interactions offer a rich platform for exploring quantum phases that transcend the paradigms of spin-1/2 systems, owing to their enlarged local Hilbert spaces and the emergence of multipolar correlations. We investigate a one-dimensional spin-1 chain where quadrupolar order is promoted by two distinct mechanisms: conventional bilinear-biquadratic exchange and bond-directional antiferromagnetic Kitaev frustration. Using density matrix renormalization group calculations, we determine the complete ground-state phase diagram and uncover two emergent phases induced by the Kitaev interaction: a Kitaev nematic phase and a Kitaev-dimer phase. The Kitaev nematic phase emerges from a fragile biquadratic dimer state via a continuous quantum phase transition in the Ising universality class. The Kitaev dimer phase spontaneously breaks a screw symmetry to favor either $x$- or $y$-spin bonding, forming a gapped state that coexists with a crystalline order of alternating $\mathbb{Z}_2$ fluxes.