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

Fahhad H. Alharbi1,2,* and Sabre Kais1,3,†

  • 1Qatar Environment and Energy Research Institute (QEERI), Doha, Qatar
  • 2King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia
  • 3Department of Chemistry, Physics, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA

  • *falharbi@qf.org.qa
  • †kais@purdue.edu
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Phys. Rev. E 87, 043308 – Published 30 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.043308

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.

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Phys. Rev. E 87, 043308– Published 30 April, 2013
  • Received 14 December 2012

©2013 American Physical Society

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