Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice

In this paper I have mapped in detail the phase diagram of pseudo-spin-1/2 pyrochlore magnets including all symmetry-allowed nearest-neighbor anisotropic interactions. I show how to organize spins into multipole moments, whose components correspond to different irreducible representations (irreps) of the lattice point group, each corresponding to a different ground state. I then demonstrate how to invert the couplings in order to comprehensively explore all ways that the different irreps can be made degenerate, which allows me to draw a clear picture of the phase diagram and explore a variety of interesting features in it, including a special locus about which families of Hamiltonians have a non-trivial winding number.