Solitons in Quantum Spin Chains

Abstract

In this contribution we will discuss the analog of classical solitons in quantum spin chains. Strictly speaking, we will deal with the analog of solitary excitations, being interested in the manifestations of solitons in real physical systems more than in the properties of solitons in a rigorous mathematical sense. From a physical point of view, solitons in magnetic systems are more or less literally equivalent to domain walls and we will use frequently this intuitive picture. The motivation for our interest is that the role of solitons in realistic spin chains has been established as an important one in the last decade both experimentally and theoretically (see several recent reviews, e.g. Izyumov 1988, Mikeska and Steiner 1990). The overwhelming majority of theoretical approaches in this context is based on a treatment of spin chains in the classical limit, although systems of experimental interest have rather low values of the spin magnitude S: S = 1/2 in CsCoCl3 and CHAB, S = 1 in CsNiF3 and S = 5/2 in TMMC. Therefore interest has grown to clarify the role of solitary excitations as elementary excitations also for spin chains with finite and even small values of S. In this article we will deal mostly with spin chains with S = 1/2 and our main example will be the Ising chain in a transverse field; however, at first sight, solitary excitations in classical spin chains appear to differ significantly from those in spin chains with spin S = 1/2, and therefore also the approach to the classical limit, varying S from 1/2 to ∞ is of substantial interest.KeywordsDomain WallIsing ModelSpin ChainSpin WaveClassical LimitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.