Z. Phys. B - Condensed Matter 77, 119-127 (1989) Condensed Zeitsehrift Matter for Physik B ?9 Springer-Verlag 1989 Quantum fluctuations in Sine-Gordon like magnetic chains: corrections to soliton energies H.-J. Mikeska ~, B. Vaz da Costa I *, and H.C. Fogedby z 1 Institut fiir Theoretische Physik, Universitfit Hannover, Federal Republic of Germany 2 Institute of Physics, University of Aarhus, Denmark Received May 11, 1989 The effect of quantum fluctuations on solitons in the easy-plane ferromagnetic chain is considered within the semiclassical approximation. In accordance with the low tempera- ture ideal gas picture we treat the solitons as a Boltzmann gas and impose quantisation on the spin wave spectrum. We present a method which allows to calculate quantum corrections in a systematic perturbation expansion in 1/S, where S is the spin length. We use this method to obtain the soliton energy to second order at zero temperature. Our results indicate that the semiclassical approach reasonably describes quantum effects on soliton properties. 1. Introduction The theoretical investigation of soliton induced prop- erties in sine-Gordon (sG) like magnetic chain systems has turned from the early qualitative approach El] to a more quantitative treatment [2-6] in recent years. This development was to large extent due to a series of detailed experiments on CsNiF3, measur- ing the neutron scattering cross section [71 and the soliton contribution to the specific heat [8]. In partic- ular the specific heat measurements lead to the con- clusion that a classical description is inadequate for CsNiF 3 (and similarly for CHAB [93) and that in- stead the combined effect of quantum corrections and out-of-plane fluctuations has to be taken into account if one aims at quantitative agreement [4]. In this paper, which is the first in a series of publications, we will present a method which allows to calculate quantum corrections to soliton induced properties in a systematic perturbation theory in 1/S, where S is the spin length and apply this method to a calculation of the soliton energy to second order at zero tempera- ture. * Permanent address: Department of Physics, University of Minas Gerais, Belo Horizonte, Brazil We take as our basic model the Hamiltonian which for S = 1 describes CsNiF3 in an external mag- netic field: A S z 2 H=--JZS. S,+~+ Z(,)--ItBZS;" (1.1) n rl A > 0 is the single site anisotropy leading to planar behaviour and we will consider ferromagnetic cou- pling, J > 0, only. In order to make use of standard fieldtheoretic arguments we must first transcribe the model (1.1) to a manageable standard fieldtheoretic model subject to canonical quantization rules. This is achieved by means of the Villain transformation [10] s / = e i*~ l/s (s + 1)- s. + 1) (1.2) where the longitudinal spin component S z and the azimuthal phase 4~, now satisfy the canonical commu- tation relation [4~m, S~] =i6m,. (1.3) The phase 4~m is a cyclic variable and its spectrum is defined modulo 2 re.
