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

TL;DR

This paper develops a tensor network approach to simulate the two-dimensional lattice $ =1$ Wess-Zumino model, enabling sign-problem-free calculations of its partition function and including interactions between Majorana fermions and scalar bosons.

Contribution

It introduces a tensor network formulation for the model with Yukawa interactions, improving existing methods and enabling numerical analysis without the sign problem.

Findings

Tensor network representation of the model constructed

Partition function computed without sign problem

Numerical results demonstrating method viability

Abstract

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.