## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

4-1-1973

#### Publication Source

Physical Review B

#### Volume

7

#### Issue

7

#### Start Page

3166

#### Last Page

3187

#### DOI

10.1103/PhysRevB.7.3166

#### Abstract

The one-dimensional alternating antiferromagnet with *H*=2*J*Σ_{n}S⃗ _{2n}⋅S⃗_{2n−1}+2*J′*Σ_{n}S⃗_{2n}⋅S⃗_{2n+1} is studied for *J′*≪*J*. For β^{−1}≡k_{B}*T*≪*J* the susceptibility is expanded in powers of the exciton density as χT∝ A (β*J′*, *J′*/*J*)e^{−2βJ} + B(β*J′*,*J′*/*J*)e^{−4βJ}+⋯ and the coefficients A and B are calculated for *J′*/*J*→0. The calculation of B(β*J′*,0) required the evaluation of the two-exciton scattering matrix. The interactions between excitons which affect the susceptibility are found to be repulsive. As a result, the coefficient B is correctly predicted by the usual assumption that excitons obey localized statistics. A general discussion relating statistics to the on-shell forward-scattering *t* matrix enables one to understand the difference between the statistical properties of spin waves and excitons. For opposite-spin excitons an attractive bound state is found to exist for all values of total momentum. Perturbation theory in *J′*/*J* is used to calculate the single-exciton dispersion relation at zero temperature as E(*k*) = (2*J*+5*J'*^{3}/32*J*^{2}) − (*J′*+*J'*^{2}/2*J*−5*J'*^{3}/32*J*) cos*k* − (*J'*^{2}/4*J*+*J'*^{3}/8*J*^{2}) cos^{2}*k* − (*J'*^{3}/8*J*^{2})cos^{3}*k*.

#### Recommended Citation

Harris, A.
(1973).
Alternating Linear Heisenberg Antiferromagnet: The Exciton Limit.
*Physical Review B,*
*7*
(7),
3166-3187.
http://dx.doi.org/10.1103/PhysRevB.7.3166

**Date Posted:** 12 August 2015

This document has been peer reviewed.