Floating, critical, and dimerized phases in a frustrated spin- 3/2 chain

We study spontaneous dimerization and emergent criticality in a spin-3/2 chain with antiferromagnetic nearest-neighbor J1, next-nearest-neighbor J₂, and three-site J₃ interactions. In the absence of three-site interaction J₃, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of J₂/J₁, going successively through a critical-commensurate phase, a partially dimerized gapped phase, a critical floating phase with quasi-long-range incommensurate order, to end up in a fully dimerized phase at very large J₂/J₁. In the field-theory language, this implies that the coupling constant of the marginal operator responsible for dimerization changes sign three times. For large enough J₃, the fully dimerized phase is stabilized for all J₂, and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2)₃ along part of the boundary and turn first order at some point due to the presence of a marginal operator in the WZW SU(2)₃ model. By contrast, the transition between the two-dimerized phase is always first order, and the phase transitions between the partially dimerized phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the intriguing spin-1/2 edge states that emerge in the partially dimerized phase for even chains. Unlike their counterparts in the spin-1 chain, they are not confined and disappear upon increasing J₂ in favor of a reorganization of the dimerization pattern.