Convergent perturbation theory for lattice models with fermions

TL;DR

This paper develops a convergent perturbation theory for lattice models with fermions by using bosonization, overcoming the divergence issues of standard perturbation methods in quantum field theory.

Contribution

It introduces a novel convergent perturbation approach for fermionic lattice models through bosonization, extending previous bosonic-focused methods.

Findings

Constructed a convergent series for a fermionic-bosonic lattice model.

Demonstrated the applicability of the method to a toy model.

Provided a framework for regularized perturbation series with infinite radius of convergence.

Abstract

The standard perturbation theory in QFT and lattice models leads to asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.