Abstract
We combine the finite-size scaling method with the mesh-free spectral method to calculate quantum critical parameters for a given Hamiltonian. The basic idea is to expand the exact wave function in a finite exponential basis set and extrapolate the information about system criticality from a finite basis to the infinite basis set limit. The used exponential basis set, though chosen intuitively, allows handling a very wide range of exponential decay rates and calculating multiple eigenvalues simultaneously. As a benchmark system to illustrate the combined approach, we choose the Hulthen potential. The results show that the method is very accurate and converges faster when compared with other basis functions. The approach is general and can be extended to examine near-threshold phenomena for atomic and molecular systems based on even-tempered exponential and Gaussian basis functions.
Keywords
TEMPERED ATOMIC ORBITALS; PARTIAL-DIFFERENTIAL-EQUATIONS; SURFACE-WAVE SIMULATIONS; MOLECULAR CALCULATIONS; SPECTRAL METHODS; EFFICIENT MODEL; ELEMENT-METHOD; SYSTEMS; BASES; APPROXIMATIONS
DOI
10.1103/PhysRevE.87.043308
Date of this Version
4-30-2013
Recommended Citation
Alberbi, Fahhad H. and Kais, Sabre, "Quantum criticality analysis by finite-size scaling and exponential basis sets" (2013). Birck and NCN Publications. Paper 1393.
http://dx.doi.org/10.1103/PhysRevE.87.043308
Comments
This is the published version of Fahhad H. Alharbi and Sabre Kais. 30 April 2013. Quantum criticality analysis by finite-size scaling and exponential basis sets. First published in the Physical Review E and is available online at: http://dx.doi.org/10.1103/PhysRevE.87.043308.