Absence of a classical long-range order in $S=1/2$ Heisenberg antiferromagnet on triangular lattice

TL;DR

This study investigates the quantum phase transition in an $S=1/2$ anisotropic Heisenberg antiferromagnet on a triangular lattice, revealing the absence of classical long-range order and suggesting a potential explanation for experimentally observed spin liquids.

Contribution

It provides new insights into the phase diagram of the anisotropic Heisenberg model, challenging the belief that the 120° Nél order is always present in such systems.

Findings

Classical 120° Nél order exists for $ ext{alpha} \, extless\, 0.55$

Critical collinear state appears for $1/\alpha \, extless\, 0.6$

Absence of classical long-range order in certain parameter regimes

Abstract

We study the quantum phase transition of an $S=1/2$ anisotropic $\alpha$ $(\equiv J_z/J_{xy})$ Heisenberg antiferromagnet on a triangular lattice. We calculate the sublattice magnetization and the long-range helical order-parameter and their Binder ratios on finite systems with $N \leq 36$ sites. The $N$ dependence of the Binder ratios reveals that the classical 120$^{\circ}$ N\'{e}el state occurs for $\alpha \lesssim 0.55$, whereas a critical collinear state occurs for $1/\alpha \lesssim 0.6$. This result is at odds with a widely-held belief that the ground state of a Heisenberg antiferromagnet is the 120$^{\circ}$ N\'{e}el state, but it also provides a possible mechanism explaining experimentally observed spin liquids.