Electronic Structure Critical Parameters From Finite-Size Scaling

Neirotti, Juan Pablo; Serra, Pablo; Kais, Sabre

doi:10.1103/physrevlett.79.3142

Cited by 51 publications

(52 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2. This behavior is different from that of our previous results [7,8] for the heliumlike atoms where the ionization energy bends sharply to zero at the helium critical l ͑He͒ c Ӎ 1.0976. The different behavior of the energy as a function of the Hamiltonian parameter, l, suggests, an analogy with standard phase transitions in statistical mechanics, that the transition from a ground bound state to a continuum in the heliumlike atoms resemble first order phase transitions, while for lithiumlike atoms, the transition is continuous.…”

Section: (Received 4 March 1998)contrasting

confidence: 79%

“…Although there is no unique recipe to define such a sequence, in this Letter we used two methods: (i) the first order method (FOM), which can be applied if the threshold energy is known [7,17]. In this method one defines l ͑N͒ as the value in which the ground state energy in the Nth-order approximation, E ͑N͒ 0 ͑l͒, is equal to the threshold energy E T ,…”

Section: (Received 4 March 1998)mentioning

confidence: 99%

“…In atomic and molecular physics, it has been suggested that there are possible analogies between critical phenomena and singularities of the energy [2][3][4]. Analogies between symmetry breaking of electronic structure configurations and standard phase transitions have been established for many electron atoms and simple molecular systems by studying the corresponding large dimension limit Hamiltonian [5,6].Recently, we presented the finite-size scaling (FSS) method to calculate the critical parameters for electronic structure [7,8]. In statistical mechanics, the FSS method provides a way to extrapolate information obtained from a finite system to the thermodynamic limit [9,10].…”

mentioning

confidence: 99%

“…Recently, we presented the finite-size scaling (FSS) method to calculate the critical parameters for electronic structure [7,8]. In statistical mechanics, the FSS method provides a way to extrapolate information obtained from a finite system to the thermodynamic limit [9,10].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Electronic Structure Critical Parameters For the Lithium Isoelectronic Series

1998

Self Cite

View full text Add to dashboard Cite

The finite-size scaling method is used to calculate the critical parameters for the lithium isoelectronic series. The critical nuclear charge, which is the minimum charge necessary to bind three electrons, for the ground state was found to be Z c Ӎ 2. Results show that the analytical behavior of the energy as a function of the nuclear charge for lithium is completely different from that of helium. Analogy with standard phase transitions show that for helium, the transition from a bound state to a continuum is "first order," while lithium exhibits a "second order phase transition." [S0031-9007(98)06405-9] PACS numbers: 05.70.Jk The study of the critical parameters of a quantum Hamiltonian and quantum phase transitions have attracted much interest in recent years [1]. These transitions take place at the absolute zero of temperature, where phase transition means that the quantum ground state of the system changes in some fundamental way as some microscopic parameters change in the Hamiltonian. In atomic and molecular physics, it has been suggested that there are possible analogies between critical phenomena and singularities of the energy [2][3][4]. Analogies between symmetry breaking of electronic structure configurations and standard phase transitions have been established for many electron atoms and simple molecular systems by studying the corresponding large dimension limit Hamiltonian [5,6].Recently, we presented the finite-size scaling (FSS) method to calculate the critical parameters for electronic structure [7,8]. In statistical mechanics, the FSS method provides a way to extrapolate information obtained from a finite system to the thermodynamic limit [9,10]. In our applications, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. In the FSS method we assumed that the two lowest eigenvalues of the quantum Hamiltonian could be taken as the leading eigenvalues of a transfer matrix of a classical pseudosystem. The phenomenological renormalization equation was used to obtain the critical properties of the system. In this approach one has to rely on the analogy to classical statistical mechanics, a more direct finite-size scaling approach without the need to make such an analogy was established by a systematic expansion in a finite (truncated) basis set [11].The analytical behavior of the energy as a function of parameters for a given system has been the subject of study for many years. In particular, the study of the analytical behavior of the energy as a function of the nuclear charge, Z. Morgan and co-workers [12] have performed a 401-order perturbation calculation to resolve the controversy over the radius of convergence of the l 1͞Z expansion for the ground state energy of the heliumlike ions. Such high order calculations were necessary to study the asymptotic behavior of the perturbation series and to determine that the radius of convergence, l ‫ء‬ , is equal to l c , the critical value of l for which the Hamiltonia...

show abstract

Section: (Received 4 March 1998)contrasting

confidence: 79%

Section: (Received 4 March 1998)mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Electronic Structure Critical Parameters For the Lithium Isoelectronic Series

1998

Self Cite

View full text Add to dashboard Cite

show abstract

“…Three-body problems have been studied in a variety of context, such as three-body Coulomb systems [1][2][3], and nuclear three-body systems [4][5][6]. Efimov predicted that a system with three particles may have a large number of trimer states even when the dimer potential does not posses any bound states [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Near Threshold Effects on Recombination and Vibrational Relaxation in Efimov Systems

2016

View full text Add to dashboard Cite

We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three-body recombination rate K3 where three free atoms interact to produce an atom-dimer pair, and the relaxation rate K rel where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for K3, namely the NTR (Near Threshold Resonance) regime behavior E −2 for negative scattering lengths and the NTS (Near Threshold Suppression) regime behavior E 2 for positive scattering lengths. We also confirm a previously found oscillatory behavior of K3 at higher energy E. Finally, we find that K rel behaves as E −1 in the NTR regime.

show abstract

Critical nuclear charges forN-electron atoms

Sergeev

Kais

1999

Int. J. Quant. Chem.

Self Cite

View full text Add to dashboard Cite

One‐particle model with a spherically‐symmetric screened Coulomb potential is proposed to describe the motion of a loosely bound electron in a multielectron atom when the nuclear charge, which is treated as a continuous parameter, approaches its critical value. The critical nuclear charge, Zc, is the minimum charge necessary to bind N electrons. Parameters of the model are chosen to meet known binding energies of the neutral atom and the isoelectronic negative ion. This model correctly describes the asymptotic behavior of the binding energy in the vicinity of the critical charge, gives accurate estimation of the critical charges in comparison with ab initio calculations for small atoms, and is in full agreement with the prediction of the statistical theory of large atoms. Our results rule out the stability of doubly charged atomic negative ions in the gas phase. Moreover, the critical charge obeys the proposed inequality, N−2≤Zc≤N−1. We show that in the presence of a strong magnetic field many atomic dianions become stable. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 533–542, 1999

show abstract

Electronic Structure Critical Parameters From Finite-Size Scaling

Cited by 51 publications

References 21 publications

Electronic Structure Critical Parameters For the Lithium Isoelectronic Series

Electronic Structure Critical Parameters For the Lithium Isoelectronic Series

Near Threshold Effects on Recombination and Vibrational Relaxation in Efimov Systems

Critical nuclear charges forN-electron atoms

Contact Info

Product

Resources

About