Exact diagonalization of the S=1/2 Heisenberg antiferromagnet on finite bcc lattices to estimate properties on the infinite lattice

TL;DR

This paper uses exact diagonalization of finite bipartite bcc lattices up to 32 vertices to estimate ground state properties of the infinite lattice, achieving high accuracy in energy and magnetization.

Contribution

It introduces a method for estimating infinite lattice properties by diagonalizing finite bcc lattices and extrapolating the results, with high precision comparisons to existing methods.

Findings

Ground state energy estimate matches third order spin wave results to five parts in ten thousand.

Staggered magnetization estimate agrees within 0.25% of spin wave calculations.

Finite lattice diagonalization provides accurate extrapolation for infinite lattice properties.

Abstract

Here we generate finite bipartite body-centred cubic lattices up to 32 vertices. We have studied the spin one half Heisenberg antiferromagnet by diagonalizing its Hamiltonian on each of the finite lattices and hence computing its ground state properties. By extrapolation of these data we obtain estimates of the T = 0 properties on the infinite bcc lattice. Our estimate of the T = 0 energy agrees to five parts in ten thousand with third order spin wave and series expansion method estimates, while our estimate of the staggered magnetization agrees with the spin wave estimate to within a quarter of one percent.