Solitary Excitations in 1 ‐D Antiferromagnetic Systems with Finite Band Width

Abstract

The experimental results in quasi 1-d antiferromagnets, e.g. TMMC, CPC /I/, which suggest non-linear effects, have been interpreted as yet in terms of the antiferromagnetic Heisenberg model.Here we consider a 1 -d model with finite band width, for which we have shown recently /2 to 4/ that in continuum approximation s o l i t a j solutions exist.2) We calculate the excitation energy, and in the way like Krumhansl and Schrieffer /5/ the free energy, the static correlation function of the lattice motion, and the width of the central peak of the dynamic structure factor connected with the solitary excitations.Formerly w e have shown /4/ that the model in time-dependent mean-field approximation and in continuum limit is given by the following Lagrangian density:* with t h e condition that (a/a t ) 1 ib= 0 at the boundary of the system. X_ is 0-the Hamiltonian density and for the other notations see /l/. (Instead o f t < 0 in /1/ w e write here -t . ) In continuum limit we have R.--+ a @ and u.(t) -+ ax(5,t). The upper signs in (1) concern the antiferromagnetic case, the lower signs the ferromagnetic one. In the following we restrict ourselves to the antiferromagnetic case. Instead of the complex probability amplitudes aO-(4, t ) and 10 J 1) Linnbstr. 5, DDR-7010 Leipzig, GDR.2 ) In /2/ instead of I in ( 1 9 ) p d (20) read -I and instead of (w2 -wo) in .(221, (24), (27), and (38) read (wo -w2).

Two‐Soliton Solution in a Modified Hubbard Chain

“…Starting from an antiferromagnetic ground state order we have calculated the excitation energy, and with the dilute gas model in the same way as Krumhansl and Schrieffer [5] the free energy, the static correlation function of the lattice motion, and the width of the central peak of the dynamic structure factor connected with the one-soliton excitations [6].…”