We review recent developments in functional renormalization group (RG) methods for interacting fermions. These approaches aim at obtaining an unbiased picture of competing Fermi liquid instabilities in the low-dimensional models like the two-dimensional Hubbard model. We discuss how these instabilities can be approached from various sides and how the fermionic RG flow can be continued into phases with broken symmetry.
An improved alogorithm for the functional renormalization group and its application to the 2D Hubbard model