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Published on: August 2, 2019
Quantum criticality analysis by finite-size scaling and exponential basis sets
1Qatar Environment and Energy Research Institute (QEERI), Doha, Qatar. falharbi@qf.org.qa
Summary
Researchers developed a new quantum critical parameter calculation method using finite-size scaling and mesh-free spectral techniques. This accurate approach converges faster, offering insights into atomic and molecular systems.
Area of Science:
- Quantum mechanics
- Computational physics
- Theoretical chemistry
Background:
- Accurate calculation of quantum critical parameters is essential for understanding material properties.
- Existing methods may face limitations in convergence speed and accuracy.
Purpose of the Study:
- To develop and validate a novel computational method for determining quantum critical parameters.
- To assess the efficiency and accuracy of the proposed method using a benchmark system.
Main Methods:
- Combining the finite-size scaling method with the mesh-free spectral method.
- Expanding the wave function in a finite exponential basis set.
- Extrapolating results from a finite to an infinite basis set limit.
Main Results:
- The combined method accurately calculates quantum critical parameters.
- The approach demonstrates faster convergence compared to other basis functions.
- The Hulthen potential was used as an effective benchmark system.
Conclusions:
- The developed method is highly accurate and efficient for calculating quantum critical parameters.
- The approach is general and applicable to various atomic and molecular systems.
- Potential for examining near-threshold phenomena in quantum systems.
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