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 (KH) chain in the presence of uniaxial single-ion anisotropy D z using the density-matrix renormalization-group method. The relative strength of the Heisenberg and Kitaev interactions is parametrized by a coupling angle ϕ , defined by J = cos ϕ and K = sin ϕ . By combining energy-based diagnostics with finite-size extrapolations of order parameters and correlation functions, we obtain a comprehensive phase diagram as a function of ϕ and D z . The phase diagram contains ferromagnetic and Néel ordered phases, collinear states with four-site spin modulation, magnetically disordered or critical regimes, two Kitaev-dominated spin-liquid-like regions, and a topological Haldane phase near the Heisenberg limit. We find that the Kitaev-dominated disordered regions acquire finite parameter widths in the spin-1 model, whereas the Haldane phase is fragile against Kitaev-type anisotropy, especially for D z < 0 . Positive D z generally suppresses magnetic order and expands nonmagnetic regimes, while negative D z enhances Ising-like magnetic order. At D z = 0 , we also identify an exactly solvable point at tan ϕ = − 2 ( ϕ / π ≃ 1.6476 ) , which gives rise to a first-order transition between the Néel- z state and a four-site collinear state. 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 single-ion anisotropy and dimensionality in Kitaev-type magnets.