  I derive a dual description of lattice fermions, specifically focusing on the
t-J and Hubbard models, that allow diagrammatic techniques to be employed
efficiently in the strongly correlated regime, as well as for systems with a
restricted Hilbert space. These constructions are based on spin-charge
transformation, where the lattice fermions of the original model are mapped
onto spins and spin-less fermions. This mapping can then be combined with
Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions
with imaginary chemical potential. The resulting models do not contain any
large expansion parameters, even for strongly correlated systems. Also, they
exhibit dramatically smaller corrections to the density matrix from nonlinear
terms in the Hamiltonian. The combination of these two properties means that
they can be addressed with diagrammatic methods, including simulation
techniques based on stochastic sampling of diagrammatic expansions.
