Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets

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.

24 pages, Latex, 3 postscript figures

References in corpus (1)

• Phase Transitions in the Spin-Half J_1--J_2 Model

Cited by in corpus (8)

• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Quantum Phase Transitions of a Square-Lattice Heisenberg Antiferromagnet with Two Kinds of Nearest-Neighbour Bonds: A High-Order Coupled-Cluster Treatment
• High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
• Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems
• Sign Rules for Anisotropic Quantum Spin Systems
• Ab Initio Treatments of the Ising Model in a Transverse Field