Using the Lanczos method for exact diagonalization on systems up to 14 sites, combined with a novel phase randomization'' technique for extracting more information from these small systems, we investigate several aspects of the one-dimensional Peierls-Hubbard Hamiltonian, in the context of trans-polyacetylene: the dependence of the ground state dimerization on the strength of the electron-electron interactions, including the effects of off-diagonal'' Coulomb terms generally ignored in the Hubbard model; the phonon vibrational frequencies and dispersion relations, and the optical absorption properties, including the spectrum of absorptions as a function of photon energy. These three different observables provide considerable insight into the effects of electron-electron interactions on the properties of real materials and thus into the nature of strongly correlated electron systems. 29 refs., 11 figs.
Using the Lanczos method for exact diagonalization on systems up to 14 sites, combined with a novel phase randomization'' technique for extracting more information from these small systems, we investigate several aspects of the one-dimensional Peierls-Hubbard Hamiltonian, in the context of trans-polyacetylene: the dependence of the ground state dimerization on the strength of the electron-electron interactions, including the effects of off-diagonal'' Coulomb terms generally ignored in the Hubbard model; the phonon vibrational frequencies and dispersion relations, and the optical absorption properties, including the spectrum of absorptions as a function of photon energy. These three different observables provide considerable insight into the effects of electron-electron interactions on the properties of real materials and thus into the nature of strongly correlated electron systems. 29 refs., 11 figs.
To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.
We study the effect of electron-electron correlations on the energetics of solitons in electron-phonon models of quasi one-dimensional materials. In these combined Peierls-Hubbard models, by use of quantum Monte Carlo techniques, we (1) establish that the ground state of an odd chain, singly charged or neutral, is a soliton; (2) calculate neutral-soliton creation energies; and (3) prove that "soliton doping" persists in the presence of correlations. We discuss the relevance of our results for trans-polyacetylene.
In this second of three articles on the optical absorption of electrons in a halffilled Peierls-distorted chain we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction U we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of band-width W, separated by the Hubbard interaction U. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum dependent but static ground state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spindegenerate. This corresponds to the Hubbard model at temperatures large compared to the spin exchange energy.
Effects of the electron correlation on the optical absorption due to inter-band transition (CT absorption) and due to non-linear excitations (mid-gap absorption) in one-dimensional Peierls-Hubbard CDW systems are studied by using the exact diagonalization method. The correlation effect of on-site repulsion U is fairly small for both the CT and the mid-gap absorption except in the boundary region between the CDW and AF phases while the correlation effect of inter-site repulsion V is significant for both the transitions. With increasing V the CT transition is suppressed and the exciton transition grows. As to the mid-gap absorption the intensities of absorption associated with the transitions from (or to) a defect state of the non-linear excitations to (or from) a conduction- or valence-band state are enhanced strongly by the effect of V . The absorption spectrum in the AF state is also calculated. Only the lowest optically-allowed state has a large oscillator strength and hence the absorption spectrum in the AF state is very sharp compared with the CT transition in the CDW state.
In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green’s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U- J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated selfconsistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system’s response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the twofield theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential ~U , coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of ~U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries. [edited by Author]
The three-band $p\text{\ensuremath{-}}d$ model of strongly correlated electrons interacting with optical phonons via diagonal and off-diagonal electron-phonon interactions is considered within the cluster perturbation theory. In the beginning, the exact diagonalization of the Hamiltonian of a CuO4 cluster results in the construction of local polaronic eigenstates $\left|p\right\ensuremath{\rangle}$ with hole numbers nh=0,1,2 per unit cell. The intercluster hoppings and interactions are exactly written in terms of Hubbard operators ${X}_{f}^{pq}=\left|p\right\ensuremath{\rangle}\ensuremath{\langle}q|$ determined via the multielectron polaronic eigenstates $\left|p\right\ensuremath{\rangle}$ at site f. The Fermi-type single-electron quasiparticle dispersion and spectral weight are calculated for the undoped antiferromagnetic parent insulator like La2CuO4. The quasiparticle dispersion of Hubbard polarons is determined by a hybridization of the Hubbard fermion subbands with local Franck-Condon resonances so the main polaronic effect of the quasiparticle band structure is a splitting of the Hubbard bands on the number of Hubbard polaron subbands. Increasing of the EPI constant results in an increase of splitting, decrease of the subband width, transfer of the spectral weight to high-energy multiphonon excitations, and subsequent localization of the charge carriers. Herewith, the effect of such renormalization for the conduction band and the valence one differs depending on the ratio of the diagonal and off-diagonal EPI. In the framework of the GTB method, the Franck-Condon broadening of the spectral function of polaronic excitations is also reproduced for strongly correlated systems with strong electron-phonon interaction.