Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets

TL;DR

This paper uses the coupled cluster method to analyze the nodal surfaces of Heisenberg antiferromagnets on square and triangular lattices, providing new insights into their wave functions and implications for quantum Monte Carlo simulations.

Contribution

The study introduces accurate CCM estimates for Ising-expansion coefficients and proposes a heuristic rule for the triangular lattice HAF, advancing understanding of their ground-state wave functions.

Findings

CCM results align with the Marshall-Peierls sign rule for square lattices.

A heuristic rule fits CCM data for triangular lattice HAF excitations.

Localised m-body excitation coefficients are highly converged, modeling the nodal surface accurately.

Abstract

The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular lattices is studied using the coupled cluster method (CCM) technique of quantum many-body theory. The phase relations between different expansion coefficients of the ground-state wave function in an Ising basis for the square lattice HAF is exactly known via the Marshall-Peierls sign rule, although no equivalent sign rule has yet been obtained for the triangular lattice HAF. Here the CCM is used to give accurate estimates for the Ising-expansion coefficients for these systems, and CCM results are noted to be fully consistent with the Marshall-Peierls sign rule for the square lattice case. For the triangular lattice HAF, a heuristic rule is presented which fits our CCM results for the Ising-expansion coefficients of states which correspond to two-body excitations with respect to the reference state. It is also seen that Ising-expansion coefficients which describe localised, $m$-body excitations with respect to the reference state are found to be highly converged, and from this result we infer that the nodal surface of the triangular lattice HAF is being accurately modeled. Using these results, we are able to make suggestions regarding possible extensions of existing quantum Monte Carlo simulations for the triangular lattice HAF.