Application of tensor network method to two dimensional lattice N=1\mathcal{N}=1 Wess-Zumino model

We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawa-type interaction of Majorana fermions and real scalar bosons. We present some numerical results.Comment: 8 pages, 4 figures, talk presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai

Quantum Field Theories with Tensor Renormalization Group

We report recent progress on the application of the tensor renormalization group (TRG) to quantum field theories pursued by the Tsukuba group. We explain how to treat the scalar, fermion, and gauge theories with the TRG method presenting the results for the phase transitions in the (3+1)-dimensional ((3+1)$d$) complex $\phi^4$ theory at finite density, (1+1)$d$ pure U(1) lattice gauge theory with a $\theta$ term, (3+1)$d$ Nambu--Jona-Lasinio model at finite density and (1+1)$d$ and (2+1)$d$ Hubbard models at an arbitrary chemical potential. It is demonstrated that the TRG method is free from the sign problem in practical calculations and applicable to the four-dimensional models.Comment: 25 pages, 20 figures, Proceedings of the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technolog