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

Abstract

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.