The Spin-Wave Continuum of The S=1/2 Linear Heisenberg Antiferromagnet

Abstract

In the S=½ linear Heisenberg antiferromagnet (HB AF)

$$H = J\sum\limits_{{i = 1}}^{N} {{{{\vec{S}}}_{i}}.} {{\vec{S}}_{{i + 1}}} - h\sum\limits_{{i = 1}}^{N} {S_{i}^{Z}}$$

((1))

although investigated by various theoretical approaches -many important questions concerning the statics and the dynamics have remained open. Recent low-temperature neutron-scattering experiments on CuCl₂•2N(C₅H₅) (CPC), which is a good realization of an S=½ HB AF chain, provided new important information on the dynamics of the system, such as lineshapes and the behaviour in a magnetic field /1/. The important quantity for direct comparison with experiments of this kind is the dynamic spin-correlation function in (q,ω) -space. It is the Fourier transform of <S^Z (l, t) S^z (l′, o) >, and for T=o it can be written as

$${{G}_{{zz}}}(q,\omega ) = \sum\nolimits_{\lambda } {{{M}_{\lambda }}} \delta (\omega + {{E}_{O}} - {{E}_{\lambda }}),{{M}_{\lambda }} = 2\pi \left| { < o} \right|\left| {{{S}^{Z}}(q)} \right|{{\left| {\lambda > } \right|}^{2}}$$

((2))