Quantum Skyrmion Research Articles

Overlap integral for quantum skyrmions

Making use of the method of spin coherent states, we obtained an analytical form of the overlap integral for quantum skyrmions.

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.

A model for doping in high-temperature superconductors

A continuum model for the process of doping in high-temperature superconductors is presented. It is shown that the introduction of dopants produces the creation of skyrmion topological excitations on the antiferromagnetic background as has been proposed before. In the present model, this happens because the equations of motion produce a constraint identifying the dopant and skyrmion positions. The quantum skyrmion energy as a function of doping is obtained from the large distance behavior of the quantum skyrmion correlation function which is evaluated at zero temperature. The destruction of the antiferromagnetically ordered Néel ground state occurs for a critical value δ C of the doping parameter for which the skyrmion energy vanishes. The model predicts a value of the critical doping given by δ C=0.39±0.03 for YBCO, which agrees with the experimental value δ C exp=0.41±0.02.

Stability and representation dependence of the quantum skyrmion

A constructive realization of Skyrme's conjecture that an effective pion mass ``may arise as a self-consistent quantal effect'' based on an ab initio quantum treatment of the Skyrme model is presented. In this quantum-mechanical Skyrme model the spectrum of states with $I=J,$ which appears in the collective quantization, terminates without any infinite tower of unphysical states. The termination point depends on the model parameters and the dimension of the SU(2) representation. Representations, in which the nucleon and ${\ensuremath{\Delta}}_{33}$ resonance are the only stable states, exist. The model is developed for both irreducible and reducible representations of general dimension. States with spin larger than 1/2 are shown to be deformed. The representation dependence of the baryon observables is illustrated numerically.