Low-Rank Quantics Tensor Train Representations of Feynman Diagrams for Multiorbital Electron-Phonon Models

Area of Science:

• Computational Physics
• Quantum Many-Body Theory
• Materials Science

Background:

• Feynman diagrams are crucial for simulating strongly correlated electron systems.
• Stochastic quantum Monte Carlo methods face the sign problem, especially for multiorbital models.
• Tensor cross interpolation (TCI) and quantics tensor train (QTT) offer efficient numerical treatments for Feynman diagrams.

Purpose of the Study:

• To address the challenge of identifying low-rank structures in Feynman diagrams for multiorbital electron-phonon systems.
• To overcome the ergodicity problem in traditional TCI algorithms for multiorbital spaces.
• To develop a more efficient numerical integration method for complex quantum systems.

Main Methods:

• Incorporation of a global search algorithm to resolve TCI ergodicity issues.
• Combination of the global search algorithm with the quantics tensor train (QTT) representation.
• Application to weak-coupling Feynman diagrams in multiorbital electron-phonon systems.

Main Results:

• Successfully identified low-rank structures in Feynman diagrams.
• Achieved efficient numerical integration with exponential time resolution.
• Demonstrated faster-than-power-law error convergence relative to computational cost.
• Eliminated the need for discontinuous region division required in non-QTT TCI.

Conclusions:

• The novel global search combined with QTT provides an efficient and robust method for simulating strongly correlated electron systems.
• This approach significantly improves the numerical treatment of Feynman diagrams, particularly for multiorbital systems.
• The method offers enhanced accuracy and computational efficiency compared to traditional techniques.