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I derive a dual description of lattice fermions, specifically focusing on thet-J and Hubbard models, that allow diagrammatic techniques to be employedefficiently in the strongly correlated regime, as well as for systems with arestricted Hilbert space. These constructions are based on spin-chargetransformation, where the lattice fermions of the original model are mappedonto spins and spin-less fermions. This mapping can then be combined withPopov-Fedotov fermionisation, where the spins are mapped onto lattice fermionswith imaginary chemical potential. The resulting models do not contain anylarge expansion parameters, even for strongly correlated systems. Also, theyexhibit dramatically smaller corrections to the density matrix from nonlinearterms in the Hamiltonian. The combination of these two properties means thatthey can be addressed with diagrammatic methods, including simulationtechniques based on stochastic sampling of diagrammatic expansions.

Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems