CPM Seminar

Macroscopic spin tunnelling and the ground state of an easy axis system with an exchange interaction

Manu Paranjape

Université de Montréal

We study a simple Hamiltonian of two, large, equal, coupled spins, of total spin s, which are subject to an external easy axis potential and a standard exchange coupling. In the absence of the coupling, the ground state is four fold degenerate, corresponding to the states where the individual spins are in their highest weight or lowest weight states. The two states up-up and down-down remain exact, degenerate, eigenstates, even in the presence of the interaction. They are the ground states for a ferromagnetic coupling. For an anti-ferromagnetic coupling the ground state is non-degenerate and given by the symmetric superposition (up-down + down-up), for integer spins while the combination (up-down - down-up) for half odd integer spins. The mixing of the two states, up-down and down-up first occurs only at 2s order in perturbation theory. Indeed, we find the mixing as a consequence of macroscopic spin tunnelling via the spin coherent state path integral. The instantons are only defined for complex field configurations, and their contribution is obtainable only by deformation of the contour of path integration into the space of complex fields.