| Abstract: | Tensor Network States suggest an efficient, entanglement-based approach, for dealing with strongly correlated many-body physics. Gauged gaussian fermionic PEPS (GGfPEPS) form a class of such states, suitable for studying lattice gauge theories. Using GGfPEPS, one can construct tensor network states describing fermionic matter coupled to dynamical gauge fields, with full gauge invariance, as well as perform efficient contractions and numerical computations, in arbitrary space dimensions, when combined with Monte-Carlo techniques (in a way that is sign-problem free). I will introduce the states, their construction and analytical properties, move to some manifestation of their physical capabilities with toy models, and end with a demonstration of their numerical power, by applying them for the variational study of the ground state of Z2 and Z3 lattice gauge theories in 2+1d. |