Floating, critical, and dimerized phases in a frustrated spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> chain
Natalia Chepiga, Ian Affleck, Frédéric Mila
Abstract
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.