Bootstrap embedding for interacting electrons in phonon coherent-state mean field.

Area of Science:

• Condensed Matter Physics
• Computational Quantum Chemistry
• Materials Science

Background:

• Accurately modeling interacting electron-phonon systems is crucial for understanding material properties.
• Existing methods often struggle with computational scaling for large systems.
• Developing efficient and accurate theoretical frameworks remains an active research area.

Purpose of the Study:

• To develop a novel computational framework for the ground state of interacting electrons coupled to a phonon mean field.
• To enable efficient treatment of large lattice systems in electron-phonon interactions.
• To provide a computationally advantageous alternative to existing methods like DMRG.

Main Methods:

• A Fermi-Bose bootstrap embedding framework combining electron correlation with phonon mean-field treatment.
• Self-consistent coherent-state mean-field approach for phonons.
• Modeling the system as correlated electrons in a self-consistent potential landscape.
• Finite-size scaling to extrapolate to infinite system size.

Main Results:

• Demonstrated convergence for system sizes up to 350 sites for the 1D Hubbard-Holstein model.
• Achieved an orders-of-magnitude runtime advantage over Density Matrix Renormalization Group (DMRG) for small systems.
• Identified optimal performance in localized regimes (Mott insulator, small polaron) and limitations in delocalized regions (Peierls transition).

Conclusions:

• The developed Fermi-Bose bootstrap embedding framework is computationally efficient for large electron-phonon systems.
• The method excels in localized regimes but shows limitations where quantum phonon fluctuations are significant.
• This work provides a valuable tool for studying complex correlated materials, with potential for further refinement.