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Exact functional renormalization group (FRG) flow equations for quantumsystems can be derived directly within an operator formalism without usingfunctional integrals. This simple insight opens new possibilities for applyingFRG methods to models for strongly correlated electrons with projected Hilbertspaces, such as quantum spin models, the $t$-$J$ model, or the Hubbard model atinfinite on-site repulsion. By representing these models in terms of HubbardX-operators, we derive exact flow equations for the time-ordered correlationfunctions of the X-operators (X-FRG), which allow us to calculate theelectronic correlation functions in the projected Hilbert space of thesemodels. The Hubbard-I approximation for the single-particle Green function ofthe Hubbard model is recovered from a trivial truncation of the flow equationswhere the two-point vertex is approximated by its atomic limit. We use ourapproach to calculate the quasi-particle residue and damping in the ``hiddenFermi liquid'' state of the Hubbard model at infinite on-site repulsion wherethe Hamiltonian consists only of the projected kinetic energy.

physical review. b./physical review. b

Functional renormalization group without functional integrals:  implementing Hilbert space projections for strongly correlated electrons via  Hubbard X-operators