Quantum kink in the continuous one-dimensional Heisenberg ferromagnet with easy plane: a picture of the antiferromagnetic magnon

Abstract

The path-integral formalism is developed to obtain the quantum spectrum of a kink in the classical continuous one-dimensional Heisenberg ferromagnet with easy plane, noting the analogy between its quantum spin 1/2 lattice version and the Heisenberg antiferromagnet of spin 1/2. From the equivalence of the spectra, the quantum kink (antikink) is identified with the antiferromagnetic magnon of spin 1/2, consistent with the recent argument by Faddeev and Takhtajan (1981). A picture of the doublet of this magnon in their claim is now given by the excitation of a pair of the kink and antikink which are stable against their mutual collision.