2D XXZ Model ground state Properties using an analytic Lanczos Expansion

Abstract

We develop the formalism for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the "t"-expansion, and spin-wave theory and series expansion methods. We find that far from the isotropic point all moment methods give essentially very similar results, but near the isotropic point the plaquette expansion is generally better than the others.

15 pages, Latex + RevTex, to appear in Phys. Rev. B

References in corpus (2)

• Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin-$\frac{1}{2}$ $XXZ$ Models
• Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

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• Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice
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• The Lanczos Algorithm for extensive Many-Body Systems in the Thermodynamic Limit
• Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice
• Arbitrary Ground State Observables from Quantum Computed Moments
• Moments-based quantum computation of the electric dipole moment of molecular systems