Competition between dimerization and vector chirality in the spin-$3/2$ J₁-J₂ Heisenberg chain with uniaxial single-ion anisotropy

The spin-$3/2$ chain is a versatile prototypical platform for the study of competition between different kinds of magnetic orders, with the objective of obtaining a deeper understanding of the corresponding quantum phase transitions. In this work, we investigate the spin-$3/2$ chain with nearest-neighbor J₁, next-nearest-neighbor J₂, and uniaxial single-ion anisotropy D terms in the absence of a magnetic field. For positive values of J₂/J₁ and D/J₁, we find seven different phases in a rich phase diagram. Without frustration J₂=0, a gapless Luttinger liquid phase remains stable for all $D>0$. As J₂ increases, we observe three phases with distinct dimerized valence bond orders, which show an intricate competition with vector chiral order and incommensurate correlations. For large J₂, regions of phase coexistence between the dimerized and vector chiral orders emerge. We present large-scale numerical data for the determination of transition lines, order parameters, and the nature of the phase transitions.