Kitaev meets AKLT in spin-3/2 honeycomb systems

Quantum disordered states, such as quantum spin liquids (QSLs), are prototypical examples of strongly entangled phases. While their properties have been studied individually, how one disordered state evolves into another remains poorly understood. In spin-3/2 honeycomb systems, the Kitaev model [1] and the Affleck–Kennedy–Lieb–Tasaki (AKLT) model [2, 3] realize distinct quantum disordered states: the Kitaev QSL and the AKLT valence-bond solid, providing a promising platform to explore such transitions. Here, we construct an interpolating Hamiltonian connecting these models and analyze its ground state using three complementary approaches incorporating quantum fluctuations at different levels: classical O(3) analysis, semi-classical SU(4) coherent state framework, and exact diagonalization. We find that the interpolation destabilizes both Kitaev and AKLT states and gives rise to diverse magnetic phases. Notably, in the frustrated region between the ferromagnetic Kitaev QSL and the AKLT state, the phase diagram reveals intricate competing phases and evolves systematically as quantum fluctuations are progressively incorporated. These results highlight how quantum fluctuations reshape the landscape between distinct disordered states, offering new insights into phase transitions among quantum disordered phases.

[1] A. Kitaev, Ann. Phys. 321, 2 (2006).

[2] I. Affleck et al., Phys. Rev. Lett. 59, 799 (1987).

[3] I. Affleck et al., Commun. Math. Phys. 115, 477 (1988).