  We present multiloop flow equations in the functional renormalization group
(fRG) framework for the four-point vertex and self-energy, formulated for a
general fermionic many-body problem. This generalizes the previously introduced
vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403
(2018)] and provides the necessary corrections to the self-energy flow in order
to complete the derivative of all diagrams involved in the truncated fRG flow.
Due to its iterative one-loop structure, the multiloop flow is well-suited for
numerical algorithms, enabling improvement of many fRG computations. We
demonstrate its equivalence to a solution of the (first-order) parquet
equations in conjunction with the Schwinger-Dyson equation for the self-energy.
