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

TL;DR

This paper introduces an analytic Lanczos (plaquette) expansion method to compute ground state properties of the 2D XXZ model, demonstrating improved accuracy near the isotropic point compared to other techniques.

Contribution

The paper develops a new analytic plaquette expansion formalism for calculating expectation values in lattice Hamiltonians, with applications to the 2D XXZ model.

Findings

The plaquette expansion outperforms other methods near the isotropic point.

Ground state energy and magnetization are accurately computed across anisotropy parameters.

The method provides a reliable alternative to existing moment-based techniques.

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.