Going beyond the Cumulant Approximation: Power Series Correction to the Single-Particle Green's Function in the...

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Strongly Correlated Electron Systems

Background:

• The Holstein model describes electron-boson interactions, crucial for understanding phenomena like superconductivity.
• Accurately calculating the single-particle Green's function is essential for characterizing electronic properties.
• Cumulant approximations offer a computationally tractable approach but have limitations in strongly correlated systems.

Purpose of the Study:

• To develop a general method for correcting the single-particle Green's function in a single-electron two-orbital Holstein system.
• To systematically analyze and derive various cumulant approximations using the power series correction (PSC) scheme.
• To compare the accuracy of the PSC method against cumulant and exact diagonalization methods across different physical regimes.

Main Methods:

• Development of a general power series correction (PSC) scheme.
• Derivation of different cumulant approximation flavors within the PSC framework.
• Comparative analysis of spectral functions obtained from PSC, cumulant approximations, and exact diagonalization.

Main Results:

• The PSC scheme provides a robust method for correcting the single-particle Green's function.
• Three distinct regimes of the Holstein system were identified, with varying performance of cumulant approximations.
• PSC spectral functions demonstrate excellent agreement with exact diagonalized spectral functions across all regimes, within spectral broadening.

Conclusions:

• The PSC method offers a significant improvement over standard cumulant approximations for the single-particle Green's function.
• The study elucidates the limitations of cumulant approximations in specific regimes of the Holstein model.
• PSC provides a reliable tool for investigating electron-boson interactions in complex quantum systems.