Mean-field description of topological charge 4e superconductors

BCS superconductors can be understood by a mean-field approximation of two-body interacting Hamiltonians, whose ground states break charge conservation spontaneously by allowing non-vanishing expectation values of charge 2e Cooper pairs. Topological superconductors, such as one-dimensional $p$-wave wires, have non-trivial ground states that support robust gapless boundary excitations. We construct a four-body Hamiltonian in one dimension and perform a mean-field analysis. The mean-field Hamiltonian is now quartic in fermions but is still exactly solvable. The ground state exhibits 4-fermion expectation values instead of Cooper pair ones. There also exists a topological phase, where the charge 4e superconductor carries exotic zero energy boundary excitations.