Optical conductivity of the half-filled hubbard chain

Area of Science:

• Condensed matter physics
• Quantum magnetism
• Solid-state physics

Background:

• The Mott-Hubbard model describes strongly correlated electron systems.
• Understanding optical conductivity is crucial for characterizing electronic properties.

Purpose of the Study:

• To determine the optical conductivity of the one-dimensional Mott-Hubbard insulator.
• To investigate the influence of coupling strengths on the absorption spectrum.

Main Methods:

• Dynamical density-matrix renormalization group (tDMRG) method for numerical analysis.
• Exact field-theoretical methods for analytical calculations at zero temperature.
• Combining analytical and numerical approaches for comprehensive results.

Main Results:

• The optical conductivity exhibits a characteristic square-root increase above the Lieb-Wu gap.
• A sharp maximum in conductivity is observed just above the gap for small to moderate interactions.
• An additional weak feature appears in the middle of the absorption band for larger interactions.

Conclusions:

• The study provides a detailed characterization of the optical conductivity in a key model system.
• Results offer insights into the behavior of one-dimensional strongly correlated insulators.
• The findings are relevant for understanding experimental optical spectra in related materials.