Two-step melting of three-sublattice order in S = 1 easy-axis triangular lattice antiferromagnets

Abstract

We consider S = 1 triangular lattice Heisenberg antiferromagnets with a strong single-ion anisotropy D that dominates over the nearest-neighbour antiferromagnetic exchange J. In this limit of small J∕D, we study low temperature (T ~ J ≪ D) properties of such magnets by employing a low-energy description in terms of hard-core bosons with nearest neighbour repulsion V ≈ 4J + J²∕D and nearest neighbour unfrustrated hopping t ≈ J²∕2D. Using a cluster Stochastic Series Expansion (SSE) algorithm to perform sign-problem-free quantum Monte Carlo (QMC) simulations of this effective model, we establish that the ground-state three-sublattice order of the easy-axis spin-density S^z(r) melts in zero field (B = 0) in a two-step manner via an intermediate temperature phase characterized by power-law three-sublattice order with a temperature dependent exponent η(T)∈[1/9,1/4]. For η(T)<2/9 in this phase, we find that the uniform easy-axis susceptibility of an L × L sample diverges as χ_L ~ L^2−9η at B = 0, consistent with recent predictions that the thermodynamic susceptibility to a uniform field B along the easy axis diverges at small B as χ_easy-axis(B)~B^{−4−18η/4−9η} in this regime.