Competition between dimerization and vector chirality in the spin-$3/2$ $J_1$-$J_2$ Heisenberg chain with uniaxial single-ion anisotropy

TL;DR

This study explores the complex phase diagram of a spin-$3/2$ Heisenberg chain with competing interactions and anisotropy, revealing seven phases and intricate transitions driven by frustration and anisotropy effects.

Contribution

It provides the first comprehensive numerical analysis of the interplay between dimerization and vector chirality in the spin-$3/2$ chain with uniaxial anisotropy, mapping out detailed phase boundaries.

Findings

Seven distinct phases identified in the phase diagram.

Competition between dimerization and vector chiral order observed.

Phase coexistence regions for large frustration levels.

Abstract

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 $J_1$, next-nearest-neighbor $J_2$, and uniaxial single-ion anisotropy $D$ terms in the absence of a magnetic field. For positive values of $J_2/J_1$ and $D/J_1$, we find seven different phases in a rich phase diagram. Without frustration $J_2=0$, a gapless Luttinger liquid phase remains stable for all $D>0$. As $J_2$ 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 $J_2$, 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.