### Abstract

Finite size scaling for calculations of the critical parameters of the few-body Schrödinger equation is based on taking the number of elements in a complete basis set as the size of the system. We show in an analogy with Yang and Lee theorem, which states that singularities of the free energy at phase transitions occur only in the thermodynamic limit, that singularities in the ground state energy occur only in the infinite complete basis set limit. To illustrate this analogy in the complex-parameter space, we present calculations for Yukawa type potential, and a Coulomb type potential for two-electron atoms.

Original language | English |
---|---|

Pages (from-to) | 45-49 |

Number of pages | 5 |

Journal | Chemical Physics Letters |

Volume | 423 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 20 May 2006 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Spectroscopy
- Atomic and Molecular Physics, and Optics
- Surfaces and Interfaces
- Condensed Matter Physics

### Cite this

*Chemical Physics Letters*,

*423*(1-3), 45-49. https://doi.org/10.1016/j.cplett.2006.03.035

**Quantum criticality at the infinite complete basis set limit : A thermodynamic analog of the Yang and Lee theorem.** / Kais, Sabre; Wenger, Craig; Wei, Qi.

Research output: Contribution to journal › Article

*Chemical Physics Letters*, vol. 423, no. 1-3, pp. 45-49. https://doi.org/10.1016/j.cplett.2006.03.035

}

TY - JOUR

T1 - Quantum criticality at the infinite complete basis set limit

T2 - A thermodynamic analog of the Yang and Lee theorem

AU - Kais, Sabre

AU - Wenger, Craig

AU - Wei, Qi

PY - 2006/5/20

Y1 - 2006/5/20

N2 - Finite size scaling for calculations of the critical parameters of the few-body Schrödinger equation is based on taking the number of elements in a complete basis set as the size of the system. We show in an analogy with Yang and Lee theorem, which states that singularities of the free energy at phase transitions occur only in the thermodynamic limit, that singularities in the ground state energy occur only in the infinite complete basis set limit. To illustrate this analogy in the complex-parameter space, we present calculations for Yukawa type potential, and a Coulomb type potential for two-electron atoms.

AB - Finite size scaling for calculations of the critical parameters of the few-body Schrödinger equation is based on taking the number of elements in a complete basis set as the size of the system. We show in an analogy with Yang and Lee theorem, which states that singularities of the free energy at phase transitions occur only in the thermodynamic limit, that singularities in the ground state energy occur only in the infinite complete basis set limit. To illustrate this analogy in the complex-parameter space, we present calculations for Yukawa type potential, and a Coulomb type potential for two-electron atoms.

UR - http://www.scopus.com/inward/record.url?scp=33646175029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646175029&partnerID=8YFLogxK

U2 - 10.1016/j.cplett.2006.03.035

DO - 10.1016/j.cplett.2006.03.035

M3 - Article

AN - SCOPUS:33646175029

VL - 423

SP - 45

EP - 49

JO - Chemical Physics Letters

JF - Chemical Physics Letters

SN - 0009-2614

IS - 1-3

ER -