Affleck, Kennedy, Lieb, and Taski (AKLT) constructed an exemplary spin-3/2 valence-bond solid (VBS) state on the hexagonal lattice, which is the ground state of an isotropic quantum antiferromagnet and possesses no spontaneous magnetization but finite correlation length. This is distinct from the Néel ordered state of the spin-3/2 Heisenberg model on the same lattice. Niggemann, Klümper, and Zittartz then generalized the AKLT Hamiltonian to one family invariant under spin rotation about the $z$ axis. The ground states of this family can be parameterized by a single parameter that deforms the AKLT state, and this system exhibits a quantum phase transition between the VBS and Néel phases, as the parameter increases from the AKLT point to large anisotropy. We investigate the opposite regime when the parameter decreases from the AKLT point and find that there appears to be a Berezinskii-Kosterlitz-Thouless-like transition from the VBS phase to an XY phase. Such a transition also occurs in the deformation of other types of AKLT states with triplet-bond constructions on the same lattice. However, we do not find such an XY-like phase in the deformed AKLT models on other trivalent lattices, such as square-octagon, cross, and star lattices. On the star lattice, the deformed family of AKLT states remain in the same phase as the isotropic AKLT state throughout the whole region of the parameter. However, for two triplet-bond generalizations, the triplet VBS phase is sandwiched between two ferromagnetic phases (for large and small deformation parameters, respectively), which are characterized by spontaneous magnetizations along different axes. Along the way, we also discuss how various deformed AKLT states can be used for the purpose of universal quantum computation.

• Received 15 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.165130