An SO(5) Topological Superfluid

The magnetic superfluid phases of Helium-3 have been identified with triplet pairing states, but as of yet no unifying theory exists to describe transitions between these states. In this work, we derive an extension of the exactly-solvable SO(5) Richardson-Gaudin model with p-wave pairing and Heisenberg interactions. This model contains topological and trivial superfluid phases, with a quartet ground state occurring at the critical SO(5)-symmetric point separating these quantum fluids. Under the influence of an external magnetic field, the ground state of this Hamiltonian retains its superfluid character with no pair breaking, exhibiting a series of transitions into a fully spin-polarized triplet state. A symmetry analysis of the ground state wavefunction is revealing.