Time dependent reduced density matrix functional theory at strong correlation: insights from a two-site Anderson...

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational chemistry

Background:

• The one-body density matrix is crucial for describing systems out of equilibrium.
• Its time evolution depends on the two-body density matrix, posing a significant challenge.
• Strong electron correlations add complexity to these calculations.

Purpose of the Study:

• To explore approximations for the two-body density matrix in strongly correlated systems.
• To investigate the time evolution of the one-body density matrix using an adiabatic approximation.
• To analyze the limitations of adiabatic approximations in the two-site Anderson impurity model.

Main Methods:

• Utilizing an adiabatic approximation based on the exact ground-state two-body density matrix.
• Studying the two-site Anderson impurity model as a specific case.
• Analyzing the imaginary part of the adiabatic approximation and its impact on N-representability.

Main Results:

• The adiabatic approximation fails to reproduce exact results, even with slow perturbation.
• Inaccurate imaginary part of the two-body density matrix approximation is identified as the cause.
• Attempts to correct the imaginary part using Hilbert transform show limited success and lead to N-representability violations.

Conclusions:

• The adiabatic approximation is insufficient for accurately describing the dynamics of the one-body density matrix in strongly correlated systems.
• Practical methods for time evolution of the one-body density matrix face constraints due to these findings.
• Further development of approximations for the two-body density matrix is necessary for accurate non-equilibrium descriptions.