Physical Review A

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

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

Published Apr 1, 1989• 20 citations

Abstract

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.

DOI: 10.1103/physreva.39.4301

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Physical Review A

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

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

Published Apr 1, 1989• 20 citations

Publisher

Abstract

DOI: 10.1103/physreva.39.4301

Related papers

Approximations to the ground-state energy of the single-impurity Kondo model using variational and connected-moments expansions

Jay D. Mancini, Janice D. Prie, William J. Massano

Physical Review AFeb 1, 199118 citations

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.

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By means of a projector operator formalism we study the ground state properties of the Anderson Impurity Hamiltonian. The non-perturbative treatment of the model agrees with the previous one, obtained by Inagaki [Prog. Theor. Phys. 62, 1441 (1979)] by means of a perturbation expansion with respect the hybridization term. We go beyond the Inagaki's formalism to the next leading order. It provides a very accurate calculation of the energy spectrum in the total spin sector and, in particular, the ground state energy in the whole parameter space. For a one body spinless system, the dependence of the ground state energy as a function of the impurity level obtained by this procedure remarkably agrees with analytical results. For the many body case the occupancy of the impurity as a function of the parameters is studied and it agrees with the corresponding one obtained by using the Bethe ansatz and the Numerical Renormalization Group solution of the Hamiltonian. The magnetization and susceptibility of the impurity is analyzed by studying the response of the system to an external magnetic field, from which it is possible to extract the Kondo temperature. The dependence of the Kondo scale with the parameters of the model is in excellent agreement with well-known results.By means of a projector operator formalism we study the ground state properties of the Anderson Impurity Hamiltonian. The non-perturbative treatment of the model agrees with the previous one, obtained by Inagaki [Prog. Theor. Phys. 62, 1441 (1979)] by means of a perturbation expansion with respect the hybridization term. We go beyond the Inagaki's formalism to the next leading order. It provides a very accurate calculation of the energy spectrum in the total spin sector and, in particular, the ground state energy in the whole parameter space. For a one body spinless system, the dependence of the ground state energy as a function of the impurity level obtained by this procedure remarkably agrees with analytical results. For the many body case the occupancy of the impurity as a function of the parameters is studied and it agrees with the corresponding one obtained by using the Bethe ansatz and the Numerical Renormalization Group solution of the Hamiltonian. The magnetization and susceptibility of the impurity is analyzed by studying the response of the system to an external magnetic field, from which it is possible to extract the Kondo temperature. The dependence of the Kondo scale with the parameters of the model is in excellent agreement with well-known results.

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Jay D. Mancini, Samuel P. Bowen, Yu Zhou

Physical review. B, Condensed matterMar 15, 19904 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.