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

TL;DR

This study uses advanced numerical methods to reveal that the easy-axis spin-1/2 XXZ antiferromagnet on a triangular lattice maintains a complex three-sublattice order, influenced by quantum fluctuations, across a broad anisotropy range.

Contribution

It provides detailed numerical evidence that the ground state remains a nontrivial three-sublattice ordered phase in the easy-axis regime, challenging simple classical expectations.

Findings

The sublattice moments stay below the classical saturation value of 1/2.

The positive sublattice moment approaches approximately 0.41873 as anisotropy increases.

The Y state is energetically favored at zero field, consistent with thermodynamic calculations.

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 $0.21671$, consistent with previous numerical estimates. In the easy-axis regime, the ordered moments remain close to a zero-magnetization three-sublattice structure of the form $(2m,-m,-m)$ over a broad range of $\Delta$. Extrapolation in $1/\Delta$ shows that the positive sublattice moment stays well below the classical saturation value $1/2$, approaching $0.41873$ as $\Delta\to\infty$, while the magnitude of the negative sublattice moment approaches $0.20832$. 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.