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Robust interpolation between weak- and strong-correlation regimes of quantum systems.
1Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland. jerzy@wmf.univ.szczecin.pl
The Journal of Chemical Physics
|February 4, 2012
Summary
This study introduces a robust interpolation method for quantum systems, accurately bridging weak and strong correlation regimes. The developed approximants precisely model energy dependence on correlation strength, proving highly accurate and versatile.
Area of Science:
- Quantum mechanics
- Computational physics
- Statistical thermodynamics
Background:
- Understanding quantum systems requires accurate models across varying correlation strengths.
- Existing methods struggle to interpolate between weak and strong correlation limits.
- Energy (E(ω)) dependence on correlation strength (ω) is crucial for many quantum phenomena.
Purpose of the Study:
- To develop a robust interpolation scheme for quantum systems.
- To create accurate approximants for energy dependence on correlation strength.
- To enable accurate modeling across weak and strong correlation regimes.
Main Methods:
- Constructing approximants based on asymptotic expansions at ω → 0 and ω → ∞ limits.
- Fitting approximants to reproduce or optimally approximate exact E(ω) values.
- Utilizing arbitrary numbers of terms and fitted parameters for flexibility.
Main Results:
- Demonstrated high accuracy of low-order approximate expressions for E(ω).
- Approximants accurately reproduce E(ω) and its derivatives.
- The method shows wide applicability in quantum systems and statistical thermodynamics.
Conclusions:
- The presented interpolation scheme offers a powerful tool for studying quantum systems.
- Accurate modeling of energy dependence is achievable across correlation strengths.
- The method is applicable to various models in physics and thermodynamics.
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