1998/06/26 by R. F. Bishop, D. J. J. Farnell, Chen Zeng · 14 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Cluster expansion #Condensed matter physics #Hexagonal lattice #Ising model #Lattice (music) #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.59.1000
published in Physical review. B, Condensed matter 59(2), 1000-1007 (American Physical Society) · 24 pages, Latex, 3 postscript figures
arxiv created 1998/06/26 · openalex publication_date 1999/01/01 · openalex created_date 2016/06/24 · arxiv updated 2017/08/24 · openalex updated_date 2026/08/05
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 localized, 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.