Superfluid and Mott insulating phases of magnons in an easy-plane ferromagnetic insulator
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In this thesis we will construct a phase diagram showing the transitions to the superfluid and Mott insulating states of magnons in an easy-plane ferromagnetic insulator with an external magnetic field applied. First we transform the Hamiltonian describing this system in several ways, to explore the basic behaviour and to obtain a boundary for the superfluid phase of these magnons. We then use a mean-field approach with the Bose-Hubbard Hamiltonian, done by van Oosten et al., "Quantum Phases in an Optical Lattice", Physical Review A 63, 053601 (2001), to find the Mott insulating regions. Finally, we scrutinize the validity of using this Hamiltonian for our system, by showing some of the different results it yields as compared to the original spin-Hamiltonian. We conclude that the obtained phase diagram is inaccurate for low spins (S=2 or lower) but significantly more reliable for high spins (S=6 and higher).