Competing magnetic and topological orders in the spin-1 Kitaev-Heisenberg chain with single-ion anisotropy

TL;DR

This study maps the complex phase diagram of the spin-1 Kitaev-Heisenberg chain with single-ion anisotropy, revealing various magnetic and disordered phases, including topological and spin-liquid states, using advanced numerical methods.

Contribution

It provides the first comprehensive phase diagram of the spin-1 Kitaev-Heisenberg chain with SIA, identifying new phases and the effects of anisotropy on magnetic order and topological states.

Findings

Identification of four magnetic order phases and three disordered regimes.

Evidence that both AFM- and FM-KSL regions have finite widths in the phase diagram.

The Haldane phase is fragile against Kitaev-type anisotropy, especially for negative D_z.

Abstract

We investigate the ground-state phase diagram of the spin-1 Kitaev--Heisenberg chain in the presence of uniaxial single-ion anisotropy (SIA) $D_z$ by density-matrix renormalization group (DMRG) calculations. By combining energy-curvature diagnostics on periodic $N=24$ clusters with a refined characterization based on order parameters and correlation functions for open chains up to $N=144$, we establish a comprehensive phase diagram in the $\phi$--$D_z$ plane. We identify four magnetically ordered phases -- FM-$z$, FM-$xy$, N\'eel-$z$, and a two-sublattice collinear LLRR2 state -- as well as magnetically disordered/critical regimes including N\'eel-$xy$, LLRR1, and two Kitaev spin-liquid (KSL) regions. A topological Haldane phase also emerges near the Heisenberg limit. Our results provide evidence that both AFM- and FM-KSL regimes acquire finite parameter widths in the spin-1 model, while the Haldane phase is fragile against Kitaev-type anisotropy, particularly for $D_z<0$. Increasing (decreasing) $D_z$ suppresses (enhances) magnetic order and expands (shrinks) the KSL and other magnetically disordered sectors. Also, at $D_z=0$, we identify an exactly solvable point at $\phi=\tan^{-1}(-2)$, which enforces a first-order transition between N\'eel-$z$ and LLRR2. We further contrast these findings with the spin-$1/2$ KH chain and with the spin-1 honeycomb KH model, highlighting the distinct roles of dimensionality and SIA in Kitaev-type magnets.