Coulomb Effects on One-Dimensional Peierls Instability: The Peierls-Hubbard Model

Mazumdar, S.; Dixit, S. N.

doi:10.1103/physrevlett.51.292

Cited by 173 publications

(49 citation statements)

References 19 publications

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“…As can be seen in Figure 2, the inclusion of the e -e interaction enhances the bond alternation at a = 0, which is the known result for homoatomic chain [6,7]. In addition, Figure 2 reveals the main feature of the Peierls distortion in the correlated system: As compared with the independent-electron model, the site-energy alternation produces a much smaller effect on the bond alternation when U > 0.…”

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confidence: 50%

Alternating charge densities, peierls distortion, and charge‐conjugation symmetry in correlated one‐dimensional diatomic systems

Kuprievich

1994

Int J of Quantum Chemistry

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The full-optimized-APSG approach based on the MC SCF technique is developed and applied to study ground-state properties of one-dimensional correlated systems. The effects of electron-electron interactions and bond relaxation are considered for the conjugated diatomic polymer; charge distribution and bond relaxation are calculated for the N = 50 chain within a wide range of site energy and e -e integral modulation involving the case of alternancy symmetry for diatomic systems. With relation to the results obtained, the problem of the neutral-ionic transition in mixed-stack crystals is discussed.

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Alternating charge densities, peierls distortion, and charge‐conjugation symmetry in correlated one‐dimensional diatomic systems

Kuprievich

1994

Int J of Quantum Chemistry

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“…As already mentioned, these results will be published elsewhere [54]. We note that in fact all other exact diagonalizations of the PPP Hamiltonian for linear polyenes were carried out using the VB formalism [12,21,87]. We must add that, of course, a great advantage of these or similar CI approaches is the fact that they are not limited to the ground states but enable us to explore the excited states at the same time [87].…”

Section: Brief Overview Of Earlier Resultsmentioning

confidence: 85%

Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene π‐electron models

Paldus

Piecuch

1992

Int J of Quantum Chemistry

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Methods accounting for correlation effects in quasi-one-dimensional rr-electron systems and based on the restricted Hartree-Fock (RHF) single determinantal reference state are briefly reviewed as well as their role in the bond length alternation (or dimerization) problem in polyacetylene-like systems, as described by the semiempirical Hamiltonians of the Pariser-ParrPople (PPP) type. Particular attention is given to the r-electron model of cyclic polyene homologous series CNHN, N = 2n = 4u + 2, Y = 1,2,. . . , which can be regarded as an idealized model of one-dimensional metallic-like systems with imposed Born-von KBrmBn boundary conditions when N -+ m. These models provide a useful bridge between the typical aromatic systems, represented by benzene (N = 6) r-electron model, and long linear polyenic chains, since the properties of these systems hardly change once a sufficiently large N (-26 or 30) is reached. It is shown that due to the quasidegenerate character of the RHF reference employed, and the related prominence of connected quadruply excited cluster components in the exact wave function, most of the standard techniques suffer a singular behavior or break down entirely for large enough systems, particularly in the strongly correlated regime. The approximate coupled pair theory that accounts for quadruply excited clusters (ACFQ method) is shown to be free of these shortcomings and is extended to include also approximately the effects of connected triexcited cluster components. These results are compared with other recently examined approximate methods accounting for the tri-and quadruply excited clusters and the proposed ACW+T(ACW) procedure is shown to provide the best results in the whole range of the coupling constant.

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“…The numerical simulation exhibits an enhancement of dimerization in the presence of repulsive interaction. 4,5,6,7,8,9) A notable finding is that the dimerization takes a maximum at a value of U being nearly the band width 5,8,9) and that the charge gap becomes much larger than the dimerization gap.5) Regarding the case of weak coupling, the analytical method of a renormalization group (RG) has also exhibited the enhancement of t d as a function of U .10) The effect of finite phonon frequency has been explored using the RG method based on the bosonization.11, 12, 13) It has been shown that the half-filled case leads to a competition between the state with both spin and charge gaps and the state with only a charge gap on the plane of the phonon frequency and the electron-phonon coupling constant.13) In contrast, the case of strong coupling with large U has been examined in terms of the opposite approach, i.e., the expansion of 1/U ) and mapping the electron system into a spin 1/2 chain system, which leads to the spin Peierls transition. The successful treatment of the quantum fluctuation leads to the occurrence of the spin Peierls transition for an arbitrary magnitude of the electron-phonon coupling constant.…”

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Correlation Effect on Peierls Transition

Sugiura

Suzumura

2002

J. Phys. Soc. Jpn.

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The effect of correlation on Peierls transition, which is accompanied by a dimerization, t d , of a bond alternation for transfer energy, has been examined for a half-filled one-dimensional electron system with on-site repulsive interaction (U ). By applying the renormalization group method to the interaction of the bosonized Hamiltonian, the dimerization has been calculated variationally and self-consistently with a fixed electron-phonon coupling constant (λ) and it is shown that t d takes a maximum as a function of U . The result is examined in terms of charge gap and spin gap and is compared with that of the numerical simulation by Hirsch [Phys. Rev. Lett 51 (1983) 296]. Relevance to the spin Peierls transition in organic conductors is discussed. KEYWORDS: Peierls transition, Hubbard model, dimerization, renormalization, charge gap, spin gapPeierls transition for a one-dimensional half-filled electron system coupled with phonon has been studied extensively since the Su-Schrieffer-Heeger model was proposed for the quasi-one-dimensional conductor polyacetylene with a bond alternation.1) The role of correlation in such a model has been examined by introducing an onsite repulsive interaction, U . The calculation using the Hartree-Fock approximation leads to the Peierls state, which exists only for U smaller than a critical value of the order of the band width.2, 3) This study has been further developed by taking into account a one-dimensional quantum fluctuation. The numerical simulation exhibits an enhancement of dimerization in the presence of repulsive interaction. 4,5,6,7,8,9) A notable finding is that the dimerization takes a maximum at a value of U being nearly the band width 5,8,9) and that the charge gap becomes much larger than the dimerization gap.5) Regarding the case of weak coupling, the analytical method of a renormalization group (RG) has also exhibited the enhancement of t d as a function of U .10) The effect of finite phonon frequency has been explored using the RG method based on the bosonization.11, 12, 13) It has been shown that the half-filled case leads to a competition between the state with both spin and charge gaps and the state with only a charge gap on the plane of the phonon frequency and the electron-phonon coupling constant.13) In contrast, the case of strong coupling with large U has been examined in terms of the opposite approach, i.e., the expansion of 1/U ) and mapping the electron system into a spin 1/2 chain system, which leads to the spin Peierls transition. The successful treatment of the quantum fluctuation leads to the occurrence of the spin Peierls transition for an arbitrary magnitude of the electron-phonon coupling constant.

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Coulomb Effects on One-Dimensional Peierls Instability: The Peierls-Hubbard Model

Cited by 173 publications

References 19 publications

Alternating charge densities, peierls distortion, and charge‐conjugation symmetry in correlated one‐dimensional diatomic systems

Alternating charge densities, peierls distortion, and charge‐conjugation symmetry in correlated one‐dimensional diatomic systems

Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene π‐electron models

Correlation Effect on Peierls Transition

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