Theory of near-zero-wave-vector neutron scattering in Haldane-gap antiferromagnets

Abstract

One-dimensional integer-spin Heisenberg antiferromagnets have disordered ground states and a gap to a triplet magnon near the antiferromagnetic wave vector, kx. Near zero wave vector the lowest energy excitation is a pair of magnons. We calculate the neutron-scattenng cross section near h = 0, using a Landau-Ginzburg model and alternatively exact S-matrix results for the O (3) nonlinear o model. The cross section is proportional to k . As a function of energy, it shows a rounded peak somewhat above the two-magnon threshold. The effects of anisotropy are also considered.

Dynamical properties of a Haldane-gap antiferromagnet

“…The physics of the O(3) nonlinear σ model is that of a triplet of massive bosons with nontrivial scattering properties. This suggests a very simple effective field theory: a free theory of three massive bosons [25]. Another route starting from an integrable model leads to an effective field theory of three massive fermions [24].…”

“…Detailed theoretical work is required to test the hypothesis that the simple model Hamiltonian (1.1) is able to reproduce the dynamical properties of NENP. Two approaches have been followed up to now: small cluster numerical studies [3][4][5][6][7][8][9][10]23] and the use of effective field theories [24,25]. The previous numerical studies were limited to spectral calculations or have ignored the presence of in-plane anisotropy.…”

Three-particle scattering continuum in quasi-one-dimensional integer-spin Heisenberg magnets

“…Using (6), it is possible to determine dynamical correlation functions within the framework of the NLσM . The q ≈ 0 behaviour of the dynamical structure factor was determined in this way by Affleck and Weston some time ago [10]. For q ≈ 0 the NLσM predicts an incoherent two magnon scattering continuum.…”

Finite-size spectrum, magnon interactions, and magnetization ofS=1Heisenberg spin chains

“…11,12 A qualitative prediction specific to the NL M is the absence of bound states. Quantitative predictions, following from the details of the magnon interactions, have also been made concerning the two- 13 and three-14 magnon contributions to the neutron-scattering cross section. However, perhaps mainly because these contributions are so small, they have, so far, not been extensively tested numerically or experimentally.…”