High-order expansion around BCS theory

TL;DR

This paper introduces a high-order diagrammatic expansion method starting from BCS theory, demonstrating its effectiveness for strongly correlated fermions in superconducting phases, including regimes with sign problems.

Contribution

It presents a generic, unbiased high-order diagrammatic approach for strongly correlated fermions, validated on the 3D attractive Hubbard model, including polarized regimes.

Findings

Convergence of the diagrammatic series up to 12 loops.

Observation of a first-order superconducting-to-normal transition.

Thermally activated polarization explained by quasiparticle theory.

Abstract

We demonstrate that summation of connected diagrams to high order starting from a BCS hamiltonian is a viable generic unbiased approach for strongly correlated fermions in superconducting or superfluid phases. For the 3D attractive Hubbard model in a strongly correlated regime, we observe convergence of the diagrammatic series, evaluated up to 12 loops thanks to the connected determinant diagrammatic Monte Carlo algorithm. Our study includes the polarized regime, where conventional quantum Monte Carlo methods suffer from the fermion sign problem. Upon increasing the Zeeman field, we observe the first-order superconducting-to-normal phase transition at low temperature, and a thermally activated polarization of the superconducting phase well described by quasiparticle theory.