Nontrivial three-sublattice magnetization in the easy-axis spin-1/2 XXZ antiferromagnet on the triangular lattice

Abstract

We investigate the ground-state magnetic structure of the spin-$1/2$ XXZ antiferromagnet on the triangular lattice in the easy-axis regime using the density-matrix renormalization group. By applying spiral boundary conditions, we exactly map finite $L\times L$ clusters onto one-dimensional chains while avoiding the spatial anisotropy inherent in cylindrical geometries. From symmetry-broken local magnetization profiles, we extract the three-sublattice moments and track their evolution with anisotropy. At the isotropic point, we obtain a positive sublattice moment of $0.217(3)$, consistent with previous numerical estimates. In the easy-axis regime ($\hat{I}”=J_z/J_{\perp }>1$), the ordered moments remain close to a Y-like zero-magnetization three-sublattice state, whose $z$-component pattern is of the form $(2m,-m,-m)$, over a broad range of $\hat{I}”$. Extrapolation in $1/\hat{I}”$ shows that the positive sublattice moment stays well below the classical saturation value $1/2$, approaching $0.419(7)$ as $\hat{I}”\to \infty$, while the magnitude of the negative sublattice moment approaches $0.209(4)$. We further compare the energies of the Y state and the up-down-down state and find that the Y state is favored at zero field. Independent thermodynamic-limit energy calculations, performed without assuming any particular ordered pattern, yield an energy consistent with the Y-state solution. These results show that the easy-axis ground state does not simply cross over to a trivially saturated collinear Ising state, but instead remains a nontrivial three-sublattice ordered state selected from the macroscopically degenerate Ising manifold by quantum fluctuations.

12 pages, 9 figures, 2 tables

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