A Study of the S=1/2 Alternating Chain using Multiprecision Methods

TL;DR

This paper investigates the ground state and excitations of the S=1/2 alternating Heisenberg antiferromagnetic chain using perturbation theory, numerical diagonalization, and novel multiprecision methods to achieve high-order analytical results.

Contribution

It introduces a novel multiprecision numerical diagonalization technique to compute high-order perturbation series for the S=1/2 alternating chain, extending known results significantly.

Findings

Ninth-order perturbation series for ground state energy and one magnon gap

Fifth-order dispersion relation and third-order neutron scattering structure factor

Numerical and analytical binding energies of two-magnon bound states

Abstract

In this paper we present results for the ground state and low-lying excitations of the $S=1/2$ alternating Heisenberg antiferromagnetic chain. Our more conventional techniques include perturbation theory about the dimer limit and numerical diagonalization of systems of up to 28 spins. A novel application of multiple precision numerical diagonalization allows us to determine analytical perturbation series to high order; the results found using this approach include ninth-order perturbation series for the ground state energy and one magnon gap, which were previously known only to third order. We also give the fifth-order dispersion relation and third-order exclusive neutron scattering structure factor for one-magnon modes and numerical and analytical binding energies of S=0 and S=1 two-magnon bound states.