Homotopic Action: A Pathway to Convergent Diagrammatic Theories

Area of Science:

• Quantum Many-Body Physics
• Computational Physics
• Theoretical Chemistry

Background:

• Feynman diagrammatic expansions struggle with slow convergence or divergence in strongly correlated systems.
• Existing methods like conformal mapping and shifted actions address specific aspects but lack universality.

Purpose of the Study:

• To introduce a universal and systematic framework, the homotopic action, for formulating convergent diagrammatic series.
• To unify existing techniques and generate new methods for solving challenging quantum systems.

Main Methods:

• Development of the homotopic action as a unifying mathematical framework.
• Application of the homotopic action to the Hubbard model as a test case.
• Demonstration of the framework's ability to eliminate resummation and introduce effective interactions.

Main Results:

• The homotopic action provides a systematic approach to achieve convergent diagrammatic series.
• The method allows for controlled ultraviolet regularization in continuous-space theories.
• It reduces the computational complexity of diagrammatic Monte Carlo methods.

Conclusions:

• The homotopic action offers a powerful and versatile tool for tackling strongly correlated many-fermion systems.
• This framework has broad implications for advancing computational approaches in quantum physics and chemistry.
• It paves the way for more accurate and efficient simulations of complex quantum phenomena.