Efficient one-loop-renormalized vertex expansions with connected determinant diagrammatic Monte Carlo

Fedor Šimkovic, IV, Riccardo Rossi, and Michel Ferrero
Phys. Rev. B 102, 195122 – Published 13 November 2020

Abstract

We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase approximation in either the particle-hole or particle-particle channels. The algorithm's efficiency is achieved by the summation over contributions of all symmetrized Feynman diagram topologies using determinants, and by integrating out analytically the two-body long-range interactions in order to yield an effective zero-range interaction. Notably, the exponential scaling of the algorithm as a function of perturbation order leads to a polynomial scaling of the approximation error with computational time for a convergent series. To assess the performance of our approach, we apply it to the nonperturbative regime of the square-lattice fermionic Hubbard model away from half-filling and report, as compared to the bare interaction expansion algorithm, significant improvements of the Monte Carlo variance as well as the convergence properties of the resulting perturbative series.

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  • Received 16 August 2020
  • Accepted 22 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.195122

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Fedor Šimkovic, IV1,2, Riccardo Rossi3,*, and Michel Ferrero1,2

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

  • *riccardorossi4@gmail.com

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Issue

Vol. 102, Iss. 19 — 15 November 2020

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