Solitons in a One-Dimensional Degenerate Hubbard Model

Abstract

Over the past few years many papers have been published on the one-dimensional systems dealing with the question whether equation of motion for them admit the existence of soliton solutions (e.g.[1-9]). One of the possible sources of nonlinearity is the electron—phonon coupling. Pushkarov et al. [4] considered a soliton formation in a ferromagnetic Heisenberg chain caused by the magnon-phonon coupling. The present paper extends the problem into itinerant system. The following discussion is stimulated by a recent discovering of quasi one-dimensional organic ferromagnets [10] which are believed to be well described by the one-dimensional doubly degenerate Hubbard model (DDH) [11]. It is well-known that molecular crystals are good candidates for the occurence of solitons. The widely discu88ed Davydov soliton [12] describing the transport of intramolecular energy and electrons along α-helical protein molecules is the best known example. Molecular crystals are mechanically soft (small elasticity coefficient) and due to the sensitivity of π-orbital overlap on the local distortion a strong electron-phonon coupling is expected. The aim of the present paper is to give a general schema of looking for the soliton solution in itinerant ferromagnets and DDH is chosen only because it is the simplest itinerant model having a ferromagnetic Hartree-Fock ground state [13, 14]. A complex question of whether these solutions represent stable