Magnetization of the spin- 12 Heisenberg antiferromagnet on the triangular lattice

Abstract

After decades of debate, now there is a rough consensus that at zero temperature the spin-$1/2$ Heisenberg antiferromagnet on the triangular lattice is three-sublattice ${120}^{\ensuremath{\circ}}$ magnetically ordered, in contrast to a quantum spin liquid as originally proposed. However, there remains considerable discrepancy in the magnetization reported among various methods. To resolve this issue, in this work we revisit this model by the tensor-network state algorithm. The ground-state energy per bond ${E}_{b}$ and magnetization per spin ${M}_{0}$ in the thermodynamic limit are obtained with high precision. The former is estimated to be ${E}_{b}=\ensuremath{-}0.18334(10)$. This value agrees well with that from the series expansion. The three-sublattice magnetic order is firmly confirmed and the magnetization is determined as ${M}_{0}=0.161(5)$. It is about $32%$ of its classical value and slightly below the lower bound from the series expansion. In comparison with the best estimated value by Monte Carlo and density-matrix renormalization group, our result is about $20%$ smaller. This magnetic order is consistent with further analysis of the three-body correlation. Our work thus provides benchmark results for this prototypical model.