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arXiv · 2010.05301

Homotopic Action: A Pathway to Convergent Diagrammatic Theories

Aaram J. Kim·Nikolay V. Prokof'ev·Boris V. Svistunov·Evgeny Kozik
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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.

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Aaram J. Kim, Nikolay V. Prokof'ev, Boris V. Svistunov, Evgeny Kozik. 2021-06-23. Homotopic Action: A Pathway to Convergent Diagrammatic Theories. https://doi.org/10.1103/physrevlett.126.257001

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