Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard-Holstein Model

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Materials Science

Background:

• The one-dimensional Hubbard-Holstein model is a key system for understanding electron-electron and electron-phonon interactions.
• Accurate theoretical descriptions are needed to capture complex phase transitions and material properties.

Purpose of the Study:

• To investigate the phase transitions in the one-dimensional Hubbard-Holstein model using Density-Matrix Embedding Theory (DMET).
• To compare the performance of DMET with Density-Matrix Renormalization Group (DMRG) and the Born-Oppenheimer (BO) approximation.

Main Methods:

• Density-Matrix Embedding Theory (DMET) was employed to study the Hubbard-Holstein model.
• Results were benchmarked against Density-Matrix Renormalization Group (DMRG) calculations.
• A comparison was made between full quantum phonon treatment and the Born-Oppenheimer (BO) approximation.

Main Results:

• A direct Peierls insulator to Mott insulator transition was observed in the adiabatic regime (slow phonons).
• A significant metallic phase was found in the anti-adiabatic regime (fast phonons), absent in the BO approximation.
• DMET results for on-site energies and excitation gaps showed good agreement with DMRG, validating the phase boundaries.

Conclusions:

• DMET accurately captures the phase diagram of the one-dimensional Hubbard-Holstein model, including crucial quantum phonon effects.
• The Born-Oppenheimer approximation fails to describe the metallic phase in the anti-adiabatic regime, highlighting the importance of quantum fluctuations.
• Quantum fluctuations of phonons are essential for understanding metallicity in this model system.