Absorption in a strong-coupling half-filled-band Hubbard chain

Lyo, S. K.; Gallinar, J. P.

doi:10.1088/0022-3719/10/10/012

Cited by 27 publications

(21 citation statements)

References 11 publications

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“…This is precisely the dependence obtained by Lyo and Galinar 30,15 for the strong coupling Hubbard model with a Neel ground state. 30,31 Again, the t-V model seems to behave as the strong coupling Hubbard model with a fixed Neel spin configuration.…”

Section: ͑63͒supporting

confidence: 85%

Exact solution of the strong couplingt−Vmodel with twisted boundary conditions

Dias¹

2000

Phys. Rev. B

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We present the solution of the one-dimensional t-V model with twisted boundary conditions in the strong coupling limit, tӶV and show that this model can be mapped onto the strong coupling Hubbard chain threaded by a fictitious flux proportional to the total momentum of the charge carriers. The high-energy eigenstates are characterized by a factorization of degrees of freedom associated with configurations of soliton and antisoliton domains and degrees of freedom associated with the movement of ''holes'' through these domains. The coexistence of solitons and antisolitons leads to a strange flux dependence of the eigenvalues. We illustrate the use of this solution, deriving the full frequency dependence of the optical conductivity at half-filling and zero temperature.

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Section: ͑63͒supporting

confidence: 85%

Exact solution of the strong couplingt−Vmodel with twisted boundary conditions

Dias¹

2000

Phys. Rev. B

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“…In Ref. [2] we showed that not only are the gross features of the spectra obtained by amplitude BCA in agreement with strong-coupling calculations [6], but in addition they show substantially more interesting detail, such as the "decoupled-dimer" peak located at ∼ U/2 + (U/2) 2 + (2t 0 ) 2 in systems with strong electron-phonon and electron-electron couplings. To emphasize the generality, in Fig.…”

Section: Amplitude Boundary Condition Averagingsupporting

confidence: 69%

Extracting Infinite System Properties from Finite Size Clusters: Phase Randomization/Boundary Condition Averaging

Gammel¹,

Campbell

Loh³

1993

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When electron-electron correlations are important, it is often necessary to use "exact" numerical methods, such as Lanczös diagonalization, to study the full many-body Hamiltonian. Unfortunately, such exact diagonalization methods are restricted to small system sizes. We show that if the Hubbard U term is replaced by a "periodic Hubbard" term, the full many body Hamiltonian may be exactly solved, even for very large systems, though for low fillings. However, for half-filled systems and large U this approach is not only no longer exact, it no longer improves extrapolation to larger systems. We discuss how generalized "randomized variable averaging" (RVA) or "phase randomization" schemes can be reliably employed to improve extrapolation to large system sizes in this regime. This general approach can be combined with any many-body method and is thus of broad interest and applicability.

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“…Compared to the charge gap, the effect of H 3 is therefore negligible in the Uӷ͉t͉ limit, and we ignore H 3 in what follows, as in previous work. [29][30][31][32][33] Any errors due to neglecting H 3 are clearly O"t i 2 /(UϪV 1 )…. We point out an important consequence of this decoupling of the N 2 ϭ1 from all other subspaces.…”

Section: Fermion To Spin Hamiltonianmentioning

confidence: 99%

“…This is the case that has been investigated previously. 27,[29][30][31][32][33]42 We consider ␦ϭ0 and ␦ 0 separately.…”

Section: Short-range Intersite Interactionmentioning

confidence: 99%

“…A much more thorough analysis of the undimerized as well as the dimerized extended Hubbard model with short-range intersite interaction has recently been presented by Gebhard et al 31,32 The models investigated by Gebhard et al were studied more recently by Yu et al, 33 who, surprisingly, obtained very different energies and bandwidths for the exciton and the electron-hole continuum. All of the above approaches [29][30][31][32][33] involve formidable algebra, and essentially involve diagonalization of the Hamiltonian within the basis of the so-called lower and upper Hubbard subbands. 34,35 For nonzero intersite interactions, the diagonalization, and the calculation of the optical absorption in particular, become rather involved.…”

Section: Introductionmentioning

confidence: 99%

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Excitons and optical absorption in one-dimensional extended Hubbard models with short- and long-range interactions

Gallagher

Mazumdar

1997

Phys. Rev. B

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We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound twomagnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the 1/r form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of -conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.

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Absorption in a strong-coupling half-filled-band Hubbard chain

Cited by 27 publications

References 11 publications

Exact solution of the strong couplingt−Vmodel with twisted boundary conditions

Exact solution of the strong couplingt−Vmodel with twisted boundary conditions

Extracting Infinite System Properties from Finite Size Clusters: Phase Randomization/Boundary Condition Averaging

Excitons and optical absorption in one-dimensional extended Hubbard models with short- and long-range interactions

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