### 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 language | English |
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Article number | 043308 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 87 |

Issue number | 4 |

DOIs | |

Publication status | Published - 30 Apr 2013 |

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### ASJC Scopus subject areas

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

### Cite this

**Quantum criticality analysis by finite-size scaling and exponential basis sets.** / Alharbi, Fahhad; Kais, Sabre.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Quantum criticality analysis by finite-size scaling and exponential basis sets

AU - Alharbi, Fahhad

AU - Kais, Sabre

PY - 2013/4/30

Y1 - 2013/4/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84877748877&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevE.87.043308

DO - 10.1103/PhysRevE.87.043308

M3 - Article

VL - 87

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 043308

ER -