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Over the last years, Projected Entangled Pair States have demonstrated greatpower for the study of many body systems, as they naturally describe groundstates of gapped many body Hamiltonians, and suggest a constructive way toencode and classify their symmetries. The PEPS study is not only limited toglobal symmetries, but has also been extended and applied for local symmetries,allowing to use them for the description of states in lattice gauge theories.In this paper we discuss PEPS with a local, SU(2) gauge symmetry, anddemonstrate the use of PEPS features and techniques for the study of a simplefamily of many body states with a non-Abelian gauge symmetry. We present, inparticular, the construction of fermionic PEPS able to describe both two-colorfermionic matter and the degrees of freedom of an SU(2) gauge field with asuitable truncation.

Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study