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