Quantized Skyrmion Fields in 2+1 Dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.Comment: Accepted for Physical Review

Large nonzero-moment magnetic strings in antiferromagnetic crystals of the manganite type

The magnetic strings in antiferromagnetic crystals with the spin $S = 1 /2$ differ from the magnetic polarons (ferrons) by the absence of the additional magnetic moment. We show that in the $S > 1 /2$ double exchange crystals with the antiferromagnetic $s-d$ exchange, a new type of magnetic strings appears, which possesses a magnetic moment. It is concentrated at the center of the string, and the magnetized string is, in its essence, the state intermediate between the string and the ferron. In antiferromagnetic manganites, this moment is by an order of magnitude larger than that of a magnetic atom. Unlike the conventional ferrons, the magnetization of the strings exists at any parameters of the crystals under consideration. We argue that this new type of magnetic state can be relevant to some doped antiferromagnets including manganites.Comment: 7 pages, 1 eps figure, RevTeX, submitted to Phys. Rev.