Optimal number of terms in QED series and its consequence in condensed matter implementations of QED

Abstract

In 1952 Dyson put forward a simple and powerful argument indicating that the perturbative expansions of QED are asymptotic. His argument can be related to Chandrasekhar's limit on the mass of a star for stability against gravitational collapse. Combining these two arguments we estimate the optimal number of terms of the QED series to be $3.1(137{)}^{3/2}\approx 5000$. For condensed matter manifestations of QED in narrow band-gap semiconductors and Weyl semimetals the optimal number of terms is around $80$ while in graphene the utility of the perturbation theory is severely limited.

arXiv comment10 pages, minor changes, version to be published in PRA. arXiv admin note: substantial text overlap with arXiv:1309.6894

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• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Wigner crystallization at large fine structure constant
• Convergent series for lattice models with polynomial interactions
• Dynamical symmetry breaking, magnetization and induced charge in graphene: Interplay between magnetic and pseudomagnetic fields