Abstract
We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group. We test the validity of the new algorithm by comparing its results with those of exact or previous methods.
Highlights
Monte Carlo simulations of lattice gauge theories have been shown successful as a nonperturbative numerical approach since the celebrated formulation by Wilson [1] and the first simulation by Creutz [2]
We conclude that Grassmann higher order tensor renormalization group (GHOTRG) is a correct algorithm
In the study of two dimensional finite chemical potential systems, we observed the very poor hierarchy of eigenvalues at μ = 1.0, and this is the reason why the accuracy gets worse around this parameter region. This shows that the situation of accuracy for GHOTRG is similar to that of the GTRG
Summary
Monte Carlo simulations of lattice gauge theories have been shown successful as a nonperturbative numerical approach since the celebrated formulation by Wilson [1] and the first simulation by Creutz [2]. The number of terms in the summation is exponentially large as a function of the system size To avoid such an expensive computational cost, one may rely on a coarse-graining of the tensor network. The original idea of TRG was limited to two dimensional systems, a new coarse-graining method suited for any higher dimensional system was proposed in Ref. We formulate HOTRG for fermions applicable to any dimensional system, and we call this Grassmann higher order tensor renormalization group (GHOTRG).
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