From the Popov-Fedotov case to universal fermionization

We show that the Popov-Fedotov trick of mapping spin-1/2 lattice systems onto two-component fermions with imaginary chemical potential readily generalizes to bosons with a fixed (but not limited) maximal site occupation number as well as to fermionic Hamiltonians with various constraints on the site Fock states. In a general case, the mapping---fermionization---is on multicomponent fermions with many-body non-Hermitian interactions. Additionally, the fermionization approach allows one to convert large many-body couplings into single-particle energies, rendering the diagrammatic series free of large expansion parameters; the latter is essential for the efficiency and convergence of the diagrammatic Monte Carlo method.