1999/02/16 by R. F. Bishop, D. J. J. Farnell, John Parkinson +1 · 3 citations
Mathematics · Physics and Astronomy · #Anisotropy #Diagonal #Geometry #Ground state #Hamiltonian (control theory) #Lattice (music) #Mathematical analysis #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Sign (mathematics) #Simple (philosophy) #Spin (aerodynamics) #Statistical physics #Wave function #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.61.6775
published as Phys. Rev. B 61 (2000), 6775-6779 · 4 pages, 1 ps-figure
arxiv created 1999/02/16 · openalex publication_date 2000/03/01 · arxiv updated 2017/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the importance of such sign rules in variational calculations and quantum Monte Carlo calculations is emphasized. This is illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.