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Journal of Physics A Mathematical and General

An approximate analytical treatment of theE⊗ε Jahn-Teller effect using Glauber states

C. C. Chancey

Published Nov 11, 1984• 12 citations
Publisher

Abstract

The octahedral Jahn-Teller system E ⊗ is studied using generalised Glauber states which are strong-coupling eigenstates of the system. It is shown that these Glauber states become, under certain conditions, equivalent to the weak-coupling eigenstates obtainable from standard perturbation theory. Eigenstates are thus obtained for the system which can be applied using perturbative procedures over the complete range of coupling strengths. Expressions which are functions of the coupling strength are obtained for the energies, the ground state Ham factor p and the A to E absorption intensities. The results compare well with the available numerical calculations.

DOI
10.1088/0305-4470/17/16/019

Related papers

Generalised Glauber states and the T1⊗(εg⊕τ2g) Jahn-Teller effect

C. C. Chancey

The octahedral Jahn-Teller system T 1 ⊗(ε g ⊕tau 2g ) is studied using generalised Glauber states which are eigenstates of the system in the strong-coupling limit. It is shown that these states become, when limited to a total angular momentum of one, eigenstates in the weak-coupling limit. The lower-branch zero-phonon state is studied using these states and expressions as functions of coupling strength are obtained for the energy and Ham reduction factors. The results compare well with the available numerical calculations.

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C. C. Chancey, Mary Claire O’Brien

The ground-state wavefunctions of the linear octahedral Jahn-Teller system T 1 ⊗(ε g ⊕ τ 2g ) are shown to exhibit a Berry phase for certain closed circuits in phonon coordinate space. This is shown to result from the coupling between the electronic and phonon parts of the system and from the requirement that the total wavefunction be single-valued. The associated Berry vector potential is also calculated and is interpreted in terms of a flux line.

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Anharmonic coherent states and E ε Jahn–Teller coupling

N.M. Avram, G. E. Drăgănescu, Calin N. Avram

The octahedral Jahn–Teller system with E [Formula: see text] ε coupling is studied in the frame of the anharmonic vibrations described by a Morse potential using anharmonic coherent states. The energy levels have been established. PACS Nos.: 31.30Gs, 71.70Ej, 42.50Ar, 42.50Ct, 33.20Wr

Canadian Journal of Physics•May 1, 2002•3 citations

OPTIMAL COUPLED-CLUSTER APPROXIMATION FOR THE E⊗(b1+b2) JAHN–TELLER EFFECT

Lezhi Lo, Chi‐Fai Lo

In this work we have applied the optimal coupled-cluster approximation to study the ground state of the E⊗(b1+b2) Jahn–Teller effect. The effectiveness of the optimal coupled-cluster approximation has been investigated for the whole range of the asymmetry parameter and various coupling strengths. It is shown that our results up to the third level of approximation are in very good agreement with the exact numerical diagonalization results and are better than those from earlier variational treatments. Furthermore, unlike previous variational treatments, the optimal coupled-cluster approximation has the advantage that the accuracy of both the ground state energy and wavefunction estimates is being taken care of and can be systematically improved. Since the mathematical treatment in this work is simple, the optimal coupled-cluster approximation could be easily extended to the studies of other fermion-boson interacting systems, e.g. the extended Jahn–Teller system.

International Journal of Modern Physics B•Dec 8, 2005•0 citations

A canonical sequence approach to the E ⊗ ε Jahn–Teller effect

Vassilios Fessatidis, Jay D. Mancini, Samuel P. Bowen +1 more

Abstract We study the linear E ⊗ ε Jahn–Teller effect in which a doubly degenerate fermionic (electron) level is coupled to a pair of degenerate oscillators. Because of the relative simplicity of the model, and since a complete numerical solution has been known for a long time, theorists have had at their disposal an excellent proving ground for a variety of calculational efforts. Here we apply the recently developed canonical sequence method (CSM) of Šamaj et al. J Phys 1997, A30, 1741 to investigate the ground state of this system. Comparisons are then made with other calculation schemes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

International Journal of Quantum Chemistry•Jan 1, 2005•3 citations

Extended projector method: Application to Jahn-Teller and pseudo-Jahn-Teller systems

Marc Vanhimbeeck, Hans A. De Raedt, D. Schoemaker

Within the Trotter-Suzuki approximations on ${e}^{\mathrm{\ensuremath{-}}\ensuremath{\beta}H}$, the extended projector method [Phys. Rev. A 36, 4612 (1987)] previously introduced by us is shown to be a valuable technique in investigating the general class of few-level systems coupled both linearly and quadratically to a selected number of harmonic oscillators. As an illustration we compare eigenvalues and Ham-reduction factors with the literature for the cubic linear Jahn-Teller systems T\ensuremath{\bigotimes}\ensuremath{\epsilon} and T\ensuremath{\bigotimes}${\ensuremath{\tau}}_{2}$ as well as for the system E\ensuremath{\bigotimes}\ensuremath{\epsilon} for which a quadratic warping interaction is included. For the latter system a symmetry projector is additionally developed, dealing with the transformation properties of nonlinear combinations of representational basis functions. As another illustration, the low-energy eigenstates of a two-level system quadratically coupled to a single harmonic oscillator are investigated. Within the ground state, the system becomes unstable at high coupling strengths and through the evaluation of time- and frequency-dependent correlation functions we found substantially different ground-state dynamic properties compared with those of a linearly coupled system.

Physical Review A•Nov 1, 1988•0 citations
The octahedral Jahn-Teller system E ⊗ is studied using generalised Glauber states which are strong-coupling eigenstates of the system. It is shown that these Glauber states become, under certain conditions, equivalent to the weak-coupling eigenstates obtainable from standard perturbation theory. Eigenstates are thus obtained for the system which can be applied using perturbative procedures over the complete range of coupling strengths. Expressions which are functions of the coupling strength are obtained for the energies, the ground state Ham factor p and the A to E absorption intensities. The results compare well with the available numerical calculations.
The octahedral Jahn-Teller system T 1 ⊗(ε g ⊕tau 2g ) is studied using generalised Glauber states which are eigenstates of the system in the strong-coupling limit. It is shown that these states become, when limited to a total angular momentum of one, eigenstates in the weak-coupling limit. The lower-branch zero-phonon state is studied using these states and expressions as functions of coupling strength are obtained for the energy and Ham reduction factors. The results compare well with the available numerical calculations.
In this work we have applied the optimal coupled-cluster approximation to study the ground state of the E⊗(b1+b2) Jahn–Teller effect. The effectiveness of the optimal coupled-cluster approximation has been investigated for the whole range of the asymmetry parameter and various coupling strengths. It is shown that our results up to the third level of approximation are in very good agreement with the exact numerical diagonalization results and are better than those from earlier variational treatments. Furthermore, unlike previous variational treatments, the optimal coupled-cluster approximation has the advantage that the accuracy of both the ground state energy and wavefunction estimates is being taken care of and can be systematically improved. Since the mathematical treatment in this work is simple, the optimal coupled-cluster approximation could be easily extended to the studies of other fermion-boson interacting systems, e.g. the extended Jahn–Teller system.
Abstract We study the linear E ⊗ ε Jahn–Teller effect in which a doubly degenerate fermionic (electron) level is coupled to a pair of degenerate oscillators. Because of the relative simplicity of the model, and since a complete numerical solution has been known for a long time, theorists have had at their disposal an excellent proving ground for a variety of calculational efforts. Here we apply the recently developed canonical sequence method (CSM) of Šamaj et al. J Phys 1997, A30, 1741 to investigate the ground state of this system. Comparisons are then made with other calculation schemes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Within the Trotter-Suzuki approximations on ${e}^{\mathrm{\ensuremath{-}}\ensuremath{\beta}H}$, the extended projector method [Phys. Rev. A 36, 4612 (1987)] previously introduced by us is shown to be a valuable technique in investigating the general class of few-level systems coupled both linearly and quadratically to a selected number of harmonic oscillators. As an illustration we compare eigenvalues and Ham-reduction factors with the literature for the cubic linear Jahn-Teller systems T\ensuremath{\bigotimes}\ensuremath{\epsilon} and T\ensuremath{\bigotimes}${\ensuremath{\tau}}_{2}$ as well as for the system E\ensuremath{\bigotimes}\ensuremath{\epsilon} for which a quadratic warping interaction is included. For the latter system a symmetry projector is additionally developed, dealing with the transformation properties of nonlinear combinations of representational basis functions. As another illustration, the low-energy eigenstates of a two-level system quadratically coupled to a single harmonic oscillator are investigated. Within the ground state, the system becomes unstable at high coupling strengths and through the evaluation of time- and frequency-dependent correlation functions we found substantially different ground-state dynamic properties compared with those of a linearly coupled system.