Floating, critical, and dimerized phases in a frustrated spin- 32 chain

We study spontaneous dimerization and emergent criticality in a spin-$\frac{3}{2}$ chain with antiferromagnetic nearest-neighbor ${J}₁$, next-nearest-neighbor ${J}₂$, and three-site ${J}₃$ interactions. In the absence of three-site interaction ${J}₃$, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of ${J}₂/{J}₁$, 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 ${J}₂/{J}₁$. 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 ${J}₃$, the fully dimerized phase is stabilized for all ${J}₂$, 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-$\frac{1}{2}$ 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 ${J}₂$ in favor of a reorganization of the dimerization pattern.