A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature

TL;DR

This paper introduces an enhanced optimization method for perturbation theory that reduces unphysical solutions and improves the accuracy of calculations for oscillator energy levels and Bose-Einstein condensation temperature shifts, aligning well with numerical simulations.

Contribution

The paper presents a novel extension of the optimized perturbation method that significantly reduces unphysical solutions and improves the accuracy of physical quantity estimations in $$ models.

Findings

Reduced number of unphysical solutions in higher-order perturbation calculations.

Accurate estimates of Bose-Einstein critical temperature shift $T_c$ matching lattice simulations.

Enhanced perturbation method applicable to various $$ models.

Abstract

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.