Tunneling series in terms of perturbation theory for quantum spin systems

Abstract

Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunnelling splitting of energy levels is reduced to constructing the perturbation series with degeneracy, the order of degeneracy being proportional to a spin value. Partial summation of this series taking into account "dangereous terms" with small denominators is performed and the value of tunnelling splitting is calcaulated with allowance for the first correction with respect to a magnetic field.

Quantum description of spin tunneling in magnetic molecules

“…From the theoretical point of view, spin tunneling has been treated mainly by the use of a WKB method adapted to spin systems [9,10], by using Feyman's path integral treatment of quantum mechanics [11,12], and also by using su(2) coherent states [13] in order to establish a correspondence between the spectrum of the spin system with the energy levels of a particle moving in an effective potential [14].…”

Tunneling of quantum rotobreathers

“…Rev. B 60, (9), p. 6212-6214 (1999) [68] It is also possible to compute the first correction to the splitting itself either by using the Rayleigh-Schrödinger perturbation theory applied to each symmetry sectors [66] or by using the Brillouin-Wigner method [67]. We have obtained…”

A new algebraization of the Laméequation

“…Finally, there are other less obvious algebraizations of the Lamé equation like, for instance, the non-standard one discussed in Ref. [16], which falls into our framework by taking…”

“…Our approach is based on the classification of one-dimensional QES potentials by González-López, Kamran, and Olver, [10], and presents some advantages over the similar algebraization considered by Ulyanov and Zaslavskii in [16].…”