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We discuss how to formulate lattice gauge theories in the Tensor Networklanguage. In this way we obtain both a consistent truncation scheme of theKogut-Susskind lattice gauge theories and a Tensor Network variational ansatzfor gauge invariant states that can be used in actual numerical computation.Our construction is also applied to the simplest realization of the quantumlink models/gauge magnets and provides a clear way to understand theirmicroscopic relation with Kogut-Susskind lattice gauge theories. We alsointroduce a new set of gauge invariant operators that modify continuouslyRokshar-Kivelson wave functions and can be used to extend the phase diagram ofknown models. As an example we characterize the transition between thedeconfined phase of the $Z_2$ lattice gauge theory and the Rokshar-Kivelsonpoint of the U(1) gauge magnet in 2D in terms of entanglement entropy. Thetopological entropy serves as an order parameter for the transition but not theSchmidt gap.

Tensor Networks for Lattice Gauge Theories with continuous groups