Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model

TL;DR

This paper presents a renormalization group improved variational perturbation method that accurately computes the mass gap in the O(2N) Gross-Neveu model, matching exact results and applicable to other models.

Contribution

It introduces a transparent, efficient extension of variational perturbation combining renormalization group properties, improving non-perturbative results for the mass gap in the Gross-Neveu model.

Findings

Reproduces exact large N mass gap at first order.

Achieves percent-level accuracy for arbitrary N using two-loop data.

Method is general and systematically improvable.

Abstract

We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a clear improvement of the non-perturbative results with respect to previous similar variational approaches. This is illustrated here by deriving optimized results for the mass gap of the O(2N) Gross-Neveu model, compared with the exactly know results for arbitrary N. At large N, the exact result is reproduced already at the very first order of the modified perturbation using this procedure. For arbitrary values of N, using the original perturbative information only known at two-loop order, we obtain a controllable percent accuracy or less, for any N value, as compared with the exactly known result for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very general and can be extended straightforwardly to any renormalizable Lagrangian model, being systematically improvable provided that a knowledge of enough perturbative orders of the relevant quantities is available.