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Analytical continuation approaches to electronic transport: the resonant level model
Eli Y Wilner1, Tal J Levy, Eran Rabani
1School of Physics and Astronomy, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
The Journal of Chemical Physics
|December 13, 2012
Summary
The Maximum Entropy (MaxEnt) method offers more accurate electric conductivity calculations than the Average Spectrum Method (ASM) for noninteracting resonant level models. This study compares both methods using Kubo formula analysis.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Computational Physics
Background:
- The Kubo formula is essential for calculating electric conductivity in materials.
- Analytical continuation methods are crucial for inferring real-frequency properties from imaginary-time data.
- Accurate spectral analysis is vital for understanding electronic transport phenomena.
Purpose of the Study:
- To compare the accuracy of the Average Spectrum Method (ASM) and Maximum Entropy (MaxEnt) for electric conductivity calculations.
- To analyze the dynamic response of a noninteracting resonant level model.
- To evaluate the performance of these methods across various temperatures, gate voltages, and lead spectral densities.
Main Methods:
- Application of the Average Spectrum Method (ASM) and Maximum Entropy (MaxEnt) to a noninteracting resonant level model.
- Utilizing the Kubo formula to determine frequency-dependent electric conductivity.
- Inferring conductivity from imaginary-time current-current correlation functions.
Main Results:
- Both ASM and MaxEnt methods were applied to calculate electric conductivity.
- Results were compared against exact solutions for validation.
- The Maximum Entropy method demonstrated superior accuracy over the Average Spectrum Method across the entire spectral range.
Conclusions:
- The Maximum Entropy method is a more reliable technique for calculating electric conductivity in this model system.
- The study highlights the importance of choosing appropriate analytical continuation methods for accurate electronic transport analysis.
- Findings provide insights into the performance of computational methods in condensed matter physics.
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