Homotopic Action: A Pathway to Convergent Diagrammatic Theories

Abstract

The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address this issue: series resummation by conformal mapping, changing the nature of the starting point of the expansion by shifted action tools, and applying the homotopy analysis method to the Dyson-Schwinger equation. They emerge as dissimilar mathematical procedures aimed at different aspects of the problem. The proposed homotopic action offers a universal and systematic framework for unifying the existing -- and generating new -- methods and ideas to formulate a physical system in terms of a convergent diagrammatic series. It eliminates the need for resummation, allows one to introduce effective interactions, enables a controlled ultraviolet regularization of continuous-space theories, and reduces the intrinsic polynomial complexity of the diagrammatic Monte Carlo method. We illustrate this approach by an application to the Hubbard model.

6 pages, 3 figures

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Cited by in corpus (13)

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• Real-frequency response functions at finite temperature
• Fast Principal Minor Algorithms for Quantum Many Body Systems
• Perturbative solution of fermionic sign problem in lattice Quantum Monte Carlo
• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
• Microscopic theory of electron quadrupling condensates
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• Solving the Bethe-Salpeter Equation in Real Frequencies at Finite Temperature
• High-temperature series expansion of the dynamic Matsubara spin correlator
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory