2017/01/10 by Tobias Pfeffer, Lode Pollet · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Diagrammatic reasoning #Homotopy #Homotopy perturbation method #Limiting #Monte Carlo method #Polynomial and algebraic computation #Quantum Information and Cryptography #Root (linguistics) #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1088/1367-2630/aa631f
published in New Journal of Physics 19(4), 043005 (IOP Publishing) · 15 pages, 18 figures, 1 table
arxiv created 2017/01/10 · openalex created_date 2017/01/26 · openalex publication_date 2017/02/27 · arxiv updated 2017/09/14 · openalex updated_date 2026/08/05
We present the construction and stochastic summation of rooted-tree diagrams, based on the expansion of a root finding algorithm applied to the Dyson–Schwinger equations. The mathematical formulation shows superior convergence properties compared to the bold diagrammatic Monte Carlo approach and the developed algorithm allows one to tackle generic high-dimensional integral equations, to avoid the curse of dealing explicitly with high-dimensional objects and to access non-perturbative regimes. The sign problem remains the limiting factor, but it is not found to be worse than in other approaches. We illustrate the method for ϕ 4 theory but note that it applies in principle to any model.