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

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8 Citations (Scopus)

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.

Original languageEnglish
Article number043308
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number4
DOIs
Publication statusPublished - 30 Apr 2013

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Finite-size Scaling
Criticality
scaling
Basis Functions
information systems
spectral methods
Threshold Phenomena
decay rates
Multiple Eigenvalues
mesh
Meshfree Method
Extrapolate
eigenvalues
Gaussian Function
Limit Set
wave functions
Spectral Methods
Exponential Decay
Decay Rate
Wave Function

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

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