Improved coarse-graining methods on two dimensional tensor networks including fermions

We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson–Majorana fermions and for the two flavor Gross–Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher’s zeros.