Title: Number-conserving interacting fermion models with exact topological superconducting ground states,
Abstract: We present a method to construct number-conserving Hamiltonians whose ground
states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such
parent Hamiltonians can be constructed not only for the usual $s$-wave BCS
state, but also for more exotic states of this form, including the ground
states of Kitaev wires and 2D topological superconductors. This method leads to
infinite families of locally-interacting fermion models with exact topological
superconducting ground states. After explaining the general technique, we apply
this method to construct two specific classes of models. The first one is a
one-dimensional double wire lattice model with Majorana-like degenerate ground
states. The second one is a two-dimensional $p_x+ip_y$ superconducting model,
where we also obtain analytic expressions for topologically degenerate ground
states in the presence of vortices. Our models may provide a deeper conceptual
understanding of how Majorana zero modes could emerge in condensed matter
systems, as well as inspire novel routes to realize them in experiment.