Renormalized perturbation theory at large expansion orders

¹ Center for Computational Quantum Physics, Flatiron Institute - 162 5th Avenue, New York, NY 10010, USA
² CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris - Route de Saclay, 91128 Palaiseau, France
³ Collège de France, 11 place Marcelin Berthelot - 75005 Paris, France

Received: 28 August 2020
Accepted: 1 September 2020

Abstract

We present a general formalism that allows for the computation of large-order renormalized expansions, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We show that this formulation compares advantageously to the currently standard techniques due to its high efficiency, simplicity, and broad range of applicability. Our formalism permits to easily complement perturbation theory with non-perturbative information, which we illustrate by implementing expansions renormalized by the addition of a gap or the inclusion of Dynamical Mean-Field Theory. As a result, we present numerically exact results for the square-lattice hole-doped Fermi-Hubbard model in the low-temperature non-Fermi-liquid regime, relevant to study the pseudogap of cuprate superconductors, and show the momentum-dependent suppression of fermionic excitations in the antinodal region.