Static versus dynamic fluctuations in the one-dimensional extended Hubbard model

Craig, H. A.; Varney, Christopher; Pickett, Warren E.; Scalettar, Richard

doi:10.1103/physrevb.76.125103

Cited by 4 publications

(3 citation statements)

References 54 publications

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“…However, that is not the case in finite systems with or without defects. A considerable confusion exists in the condensed matter community because in some cases [55,[57][58][59] Q i is included while in others [24,38,39,[60][61][62][63][64][65][66][67] it is not. Some authors, however, introduced a cutoff in the Coulomb potential in such a way that its range was shorter than the unit cell chosen to implement the periodic boundary conditions under which the system was solved [61].…”

Section: The Hubbard and Extended Hubbard Modelsmentioning

confidence: 99%

Can model Hamiltonians describe the electron–electron interaction inπ-conjugated systems?: PAH and graphene

Chiappe¹,

Louis²,

San‐Fabián³

et al. 2015

J. Phys.: Condens. Matter

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Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an 'effective' Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

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Section: The Hubbard and Extended Hubbard Modelsmentioning

confidence: 99%

Can model Hamiltonians describe the electron–electron interaction inπ-conjugated systems?: PAH and graphene

Chiappe¹,

Louis²,

San‐Fabián³

et al. 2015

J. Phys.: Condens. Matter

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“…For example, the displacements in the linear Holstein and Hubbard-Holstein models can be on the order of the lattice constant when CDW correlations are significant. [19][20][21] This can occur even for weak values of the e-ph coupling if the Fermi surface is well nested, as is the case for the Holstein model with nearest neighbor hopping on a cubic lattice. Similarly, a small polaron can be dressed by tens to hundreds of phonon quanta, 22 implying the presence of a heavily distorted lattice surrounding the carrier.…”

Section: Introductionmentioning

confidence: 96%

Quasiparticle properties of the nonlinear Holstein model at finite doping and temperature

Li¹,

Nowadnick²,

Johnston³

2015

Phys. Rev. B

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We use determinant quantum Monte Carlo to study the single particle properties of quasiparticles and phonons in a variant of the two-dimensional Holstein model that includes an additional non-linear electron-phonon (e-ph) interaction. We find that a small positive non-linear interaction reduces the effective coupling between the electrons and the lattice, suppresses charge-density wave (CDW) correlations, and hardens the effective phonon frequency. Conversely, a small negative nonlinear interaction can enhance the e-ph coupling resulting in heavier quasiparticles, an increased tendency towards a CDW phase at all fillings, and a softened phonon frequency. An effective linear model with a renormalized interaction strength and phonon frequency can qualitatively capture this physics; however, the quantitative effects of the non-linearity on both the electronic and phononic degrees of freedom cannot be captured by such a model. These results are significant for typical non-linear coupling strengths found in real materials, indicating that non-linearity can have an important influence on the physics of many e-ph coupled systems.

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“…In one dimension, the ionic Hubbard model has been widely studied through a variety of techniques including density matrix renormalization group (DMRG), exact diagonalization, bosonization and quantum Monte Carlo (QMC) with on-site 5,6,7,8 or extended 2,3,9,10,11,12 interactions. The precise conclusions are still subject to some debate, but many of the studies suggest that the direct transition from the band insulator to the Mott insula-tor is replaced by an intervening insulating bond-ordered phase.…”

Section: Introductionmentioning

confidence: 99%

Metallic phase in the two-dimensional ionic Hubbard model

et al. 2007

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We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo (DQMC). At half-filling, when the interaction strength or the staggered potential dominate we find Mott and band insulators, respectively. When these two energies are of the same order we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.

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Static versus dynamic fluctuations in the one-dimensional extended Hubbard model

Cited by 4 publications

References 54 publications

Can model Hamiltonians describe the electron–electron interaction inπ-conjugated systems?: PAH and graphene

Can model Hamiltonians describe the electron–electron interaction inπ-conjugated systems?: PAH and graphene

Quasiparticle properties of the nonlinear Holstein model at finite doping and temperature

Metallic phase in the two-dimensional ionic Hubbard model

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