Quantum criticality analysis by finite-size scaling and exponential basis sets

Fahhad H. Alberbi, QEERI; King Abdulaziz City for Science & Technology
Sabre Kais, Birck Nanotechnology Center, Purdue University

Date of this Version



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.


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.


Nanoscience and Nanotechnology