Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Conductivity measurements are vital for probing electronic systems.
• Theoretical descriptions of conductivity face challenges with strong nonlocal correlations.
• The Hubbard model is a fundamental model for understanding electron correlation effects.

Purpose of the Study:

• To analyze the conductivity of the half-filled single-band Hubbard model.
• To identify the role of spatial correlations in conductivity across the Mott transition.
• To elucidate the necessity of vertex corrections for accurate conductivity calculations.

Main Methods:

• Theoretical analysis of the Hubbard model.
• Investigation of the spectral function.
• Inclusion of multielectron processes via vertex corrections.

Main Results:

• Vertex corrections are essential for describing conductivity in the correlated metallic regime.
• The contribution of vertex corrections to dc conductivity vanishes at the Mott transition.
• Vertex corrections remain significant for optical conductivity in the Mott insulating regime.

Conclusions:

• Accurate conductivity requires both spectral function and vertex corrections, particularly in correlated systems.
• The Mott transition signifies a change in the importance of vertex corrections for different conductivity types.
• This work provides insights into the complex behavior of conductivity in strongly correlated electron systems.