Quantum fluctuations and magnetic solitons: Equivalence of discrete lattice and renormalized continuum approaches

Abstract

We discuss quantitative calculations for nonlinear excitations in one-dimensional magnets in the semiclassical regime. We show that the field-theoretic approach—calculating zero point fluctuations in the continuum limit and using counterterms to deal consistently with ultraviolet divergencies—is equivalent to calculating quantum fluctuations for a discrete lattice, if the parameters are identified properly. The latter, technically simpler approach is applied to a calculation of the reduction of soliton induced correlation functions by quantum and thermal fluctuations.