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arXiv:2604.14767 · Physical review. B./Physical review. B

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

Masahiro Kadosawa, Masaaki Nakamura, Y. Ohta, Satoshi Nishimoto

Published Jun 12, 2026• 1 citation
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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 × 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 ( Δ = J z / J ⊥ > 1 ), the ordered moments remain close to a Y-like zero-magnetization three-sublattice state, whose z -component pattern is of the form ( 2 m , − m , − m ) , over a broad range of Δ . Extrapolation in 1 / Δ shows that the positive sublattice moment stays well below the classical saturation value 1 / 2 , approaching 0.419(7) as Δ → ∞ , 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.

DOI
10.1103/lx93-brc2

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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 × 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 ( Δ = J z / J ⊥ > 1 ), the ordered moments remain close to a Y-like zero-magnetization three-sublattice state, whose z -component pattern is of the form ( 2 m , − m , − m ) , over a broad range of Δ . Extrapolation in 1 / Δ shows that the positive sublattice moment stays well below the classical saturation value 1 / 2 , approaching 0.419(7) as Δ → ∞ , 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.
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Plateaux in the magnetization curves of the square-, triangular- and hexagonal-lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero-magnetization plateau (corresponding to a spin gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one-third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer-matrix computations for the Ising limit and continue with series in the XXZ anisotropy for plateau boundaries using the ground states of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated with the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.