Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice

TL;DR

This paper computes exact spectra for the quantum Heisenberg antiferromagnet on a triangular lattice, providing evidence for Néel order, and compares numerical results with spin-wave theory, enhancing understanding of low-energy states and order parameters.

Contribution

It presents exact spectral calculations up to N=36 spins, analyzes low-lying states, and confirms Néel order through numerical and analytical methods, including boundary condition effects.

Findings

Low-lying energy levels are below the softest magnons.

Degeneration of low-energy states supports Néel order in the thermodynamic limit.

Order parameter matches spin-wave theory predictions.

Abstract

Exact spectra of periodic samples are computed up to $ N=36 $. Evidence of an extensive set of low lying levels, lower than the softest magnons, is exhibited. These low lying quantum states are degenerated in the thermodynamic limit; their symmetries and dynamics as well as their finite-size scaling are strong arguments in favor of N\'eel order. It is shown that the N\'eel order parameter agrees with first-order spin-wave calculations. A simple explanation of the low energy dynamics is given as well as the numerical determinations of the energies, order parameter and spin susceptibilities of the studied samples. It is shown how suitable boundary conditions, which do not frustrate N\'eel order, allow the study of samples with $ N=3p+1 $ spins. A thorough study of these situations is done in parallel with the more conventional case $ N=3p $.