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

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.