Higher order effective interactions and effective bosonized model for 2-N particle states

TL;DR

This paper develops an effective fermion model with higher order interactions, explores its bosonization, and investigates the role of mean field solutions, revealing approximate symmetries in weak field expansions.

Contribution

It introduces a novel higher order interaction fermion model and analyzes its bosonized form, emphasizing the significance of mean field solutions for symmetry properties.

Findings

Bosonized model exhibits approximate symmetry in weak field expansion.

Symmetry disappears when boson mean fields are set to zero.

Mean field solutions are crucial for the symmetry structure.

Abstract

In this work, an effective fermion model with particular higher order interactions given by: $I_{II} = \sum_n^N g_{2^n} (\bar{\psi}_a \psi_a)^{2^n}$, for finite $N$, is investigated by means of the auxiliary field method by taking into account 2$n$-particle states as proposed in Ref. [1]. The bosonized model was found to exhibit an approximate symmetry when expanded for weak field fluctuations around the mean field solutions. In the present work, the role of the mean field solutions for the corresponding auxiliary fields is investigated. With the integration of fermions, the resulting determinant is expanded in a polynomial boson model in the weak field approximation and the approximate symmetry found for this series does not appear if the boson mean fields are set to zero.