Physical Review A

Connected moments expansion for the ground-state energy of systems described by nonlinear Hamiltonians

Jerzy Ciosłowski

Published Jul 1, 1987• 37 citations

Abstract

An extension of the connected moments expansion to nonlinear Hamiltonians is presented. The new method enables construction of rapidly convergent series for the ground-state energy which requires a relatively small amount of numerical effort.

DOI: 10.1103/physreva.36.374

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t -expansion and connected-moment expansion: A generalization to excited states

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Application of the connected-moment expansion to single-impurity Anderson Hamiltonians

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We use the connected-moment expansion, recently developed by Cioslowski [Phys. Rev. Lett. 58, 83 (1987)], to investigate the ground-state energy of the single-impurity Anderson model. It is found that the moment expansion obtained for this Hamiltonian is not a Stieltjes series and thus does not provide a useful method for estimating ground-state energies.

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Physical Review A

Connected moments expansion for the ground-state energy of systems described by nonlinear Hamiltonians

Jerzy Ciosłowski

Published Jul 1, 1987• 37 citations

Publisher

Abstract

DOI: 10.1103/physreva.36.374

Related papers

t -expansion and connected-moment expansion: A generalization to excited states

P. Markoš, Š. Olejník

The $t$ -expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities ${M}_{n}(t)$ and ${D}_{n}(t)$ which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard $t$ -expansion, the $t$ -series for ${M}_{n}(t)$ and ${D}_{n}(t)$ are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.The $t$-expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities ${M}_{n}(t)$ and ${D}_{n}(t)$ which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard $t$-expansion, the $t$-series for ${M}_{n}(t)$ and ${D}_{n}(t)$ are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsOct 15, 19909 citations

Application of the connected-moment expansion to single-impurity Anderson Hamiltonians

William J. Massano, Samuel P. Bowen, Jay D. Mancini

Physical Review AApr 1, 198920 citations

Estimation of the overlap between the approximate and exact wave function of the ground state from the connected-moments expansion

Jerzy Ciosłowski

Physical Review AOct 1, 198719 citations

Analytic properties of connected moments expansions

Jay D. Mancini, Yu Zhou, P. F. Meier

International Journal of Quantum ChemistryApr 5, 199438 citations

Removal of the singularity in the moment-expansion formalism

Nazakat Ullah

The expression for the exact ground-state energy as given by Horn and Weinstein [Phys. Rev. D 30, 1256 (1984)] is approximated using a probability distribution function having a \ensuremath{\delta} function and a uniform distribution. The expression obtained up to second order does not have the singularity that one encounters in the connected-moment expansion. It also gives the same kind of expression for the ground-state energy that recently has been given by Mancini, Zhou, and Meier [Int. J. Quant. Chem. 50, 101 (1994)] when the third moment becomes negative.The expression for the exact ground-state energy as given by Horn and Weinstein [Phys. Rev. D 30, 1256 (1984)] is approximated using a probability distribution function having a \ensuremath{\delta} function and a uniform distribution. The expression obtained up to second order does not have the singularity that one encounters in the connected-moment expansion. It also gives the same kind of expression for the ground-state energy that recently has been given by Mancini, Zhou, and Meier [Int. J. Quant. Chem. 50, 101 (1994)] when the third moment becomes negative.

Physical Review AMar 1, 199517 citations

Self-consistent perturbative evaluation of ground-state energies: Application to cohesive energies of spin lattices

Mohamad Al Hajj, Jean‐Paul Malrieu

This work presents a simple formalism which proposes an estimate of the ground-state energy from a single reference function. It is based on a perturbative expansion but leads to nonlinear coupled equations. It can be viewed as well as a modified coupled cluster formulation. Applied to a series of spin lattices governed by model Hamiltonians the method leads to simple analytic solutions. The so-calculated cohesive energies are surprisingly accurate. Two examples illustrate its applicability to locate phase transition.This work presents a simple formalism which proposes an estimate of the ground-state energy from a single reference function. It is based on a perturbative expansion but leads to nonlinear coupled equations. It can be viewed as well as a modified coupled cluster formulation. Applied to a series of spin lattices governed by model Hamiltonians the method leads to simple analytic solutions. The so-calculated cohesive energies are surprisingly accurate. Two examples illustrate its applicability to locate phase transition.

arXiv:cond-mat/0411542Physical Review BNov 30, 20045 citations

The

t

-expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities

{M}_{n}(t)

and

{D}_{n}(t)

which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard

t

-expansion, the

t

-series for

{M}_{n}(t)

and

{D}_{n}(t)

are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.