2020/08/17 by Fedor Šimkovic, Fedor Šimkovic IV, Riccardo Rossi +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Feynman diagram #Ising model #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Renormalization #Scaling #Series expansion #Square lattice #Statistical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.195122
published as Phys. Rev. B 102, 195122 (2020) · 12 pages, 10 figures
arxiv created 2020/08/17 · openalex publication_date 2020/11/13 · arxiv updated 2020/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.