Spin Hamiltonian with large fourth order terms: triple well potentials and Bloch sphere visualization

Abstract We present a study of a general spin Hamiltonian with terms up to fourth order. The semiclassical potential is obtained as the expectation value of the parameter dependent Hamiltonian in the coherent state basis, and using catastrophe theory its parameter space is constructed. Considering the components of the magnetic field as the free parameters, we found regions where the semiclassical potential has three stability wells when the parameters of the fourth order terms are large. Using the coherent states we are able to visualize the localization of the ground state eigenfunction on the Bloch sphere as the magnetic field is varied.