Suppression of quantum tunneling for all spins for easy-axis systems

TL;DR

This paper demonstrates that quantum tunneling is suppressed for all non-zero spins in easy-axis systems, regardless of whether the kinetic term is quadratic or first order, clarifying previous misconceptions based on complex Euclidean actions.

Contribution

It proves that tunneling is suppressed for all non-zero spins in easy-axis systems with both quadratic and first order kinetic terms, resolving prior conflicting results.

Findings

Tunneling is suppressed for all non-zero spins in easy-axis systems.

Complex Euclidean action requires using complex critical points for accurate quantum theory.

Incorrect conclusions arise if complex critical points are not considered.

Abstract

The semi-classical limit of quantum spin systems corresponds to a dynamical Lagrangian which contains the usual kinetic energy, the couplings and interactions of the spins and an additional, first order kinematical term which corresponds to the Wess-Zumino-Novikov-Witten (WZNW) term for the spin degree of freedom \cite{og}. It was shown that in the case of the kinetic dynamics determined only by the WZNW term, half odd integer spin systems show a lack of tunneling phenomena whereas integer spin systems are subject to it \cite{l} in the case of potentials with easy-plane easy-axis symmetry. Here we prove, for the theory with a normal quadratic kinetic term of arbitrary strength or the first order theory with azimuthal symmetry (which is equivalently the so-called easy-axis situation), that the tunneling is in fact suppressed for all non-zero values of spin. This model exemplifies the concept that in the presence of complex Euclidean action, it is necessary to use the ensuing complex critical points in order to define the quantum (perturbation) theory \cite{ampr}. In the present example, if we do not do so, exactly the opposite, erroneous conclusion, that the tunneling is unsuppressed for all spins, is reached.