We study the complete extended Hubbard-Holstein Hamiltonian on a four-site chain with equally spaced sites, with spacing-dependent electronic interaction parameters evaluated in terms of Wannier functions built from Gaussian atomic orbitals. By successive application of generalized displacement and squeezing transformations, an effective polaronic Hamiltonian is obtained, containing a purely phonon-induced, long-range intersite charge interaction. The phase diagrams for $N=1,$ 2, 3, and 4 electrons are determined by variational minimization of the sum of the electronic and the phononic energy, paying special attention to the effects of the above-mentioned phonon-induced long-range interaction. To characterize the physics of each ground state, we evaluate how variations of the site spacing affect the behavior of several correlation functions of experimental interest, with the aim of representing lattice deformation effects, either spontaneous or induced by external pressure.We study the complete extended Hubbard-Holstein Hamiltonian on a four-site chain with equally spaced sites, with spacing-dependent electronic interaction parameters evaluated in terms of Wannier functions built from Gaussian atomic orbitals. By successive application of generalized displacement and squeezing transformations, an effective polaronic Hamiltonian is obtained, containing a purely phonon-induced, long-range intersite charge interaction. The phase diagrams for $N=1,$ 2, 3, and 4 electrons are determined by variational minimization of the sum of the electronic and the phononic energy, paying special attention to the effects of the above-mentioned phonon-induced long-range interaction. To characterize the physics of each ground state, we evaluate how variations of the site spacing affect the behavior of several correlation functions of experimental interest, with the aim of representing lattice deformation effects, either spontaneous or induced by external pressure.

arXiv:cond-mat/0010465Physical review. B, Condensed matterJan 2, 20016 citations

Bipolarons from long-range interactions: Singlet and triplet pairs in the screened Hubbard-Fröhlich model on the chain

J. P. Hague, P. E. Kornilovitch

We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent, and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent, and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.

arXiv:0904.3678Physical Review BAug 3, 200921 citations

Impact of Retardation in the Holstein-Hubbard Model: a two-site Calculation

F. Marsiglio

Eliashberg theory provides a theoretical framework for understanding the phenomenon of superconductivity when pairing between two electrons is mediated by phonons, and retardation effects are fully accounted for. However, when a direct Coulomb interaction between two electrons is also present, this interaction is only partially accounted for. In this work we use a well-defined Hamiltonian, the Hubbard-Holstein model, to examine this competition more rigorously, using exact diagonalization on a two-site system. We find that the direct electron-electron repulsion between two electrons has a significantly more harmful effect on pairing than suggested through the standard treatment of this interaction.Eliashberg theory provides a theoretical framework for understanding the phenomenon of superconductivity when pairing between two electrons is mediated by phonons, and retardation effects are fully accounted for. However, when a direct Coulomb interaction between two electrons is also present, this interaction is only partially accounted for. In this work we use a well-defined Hamiltonian, the Hubbard-Holstein model, to examine this competition more rigorously, using exact diagonalization on a two-site system. We find that the direct electron-electron repulsion between two electrons has a significantly more harmful effect on pairing than suggested through the standard treatment of this interaction.

arXiv:2205.10352May 6, 20221 citation

Effects of two-site correlations in the Hubbard model

Adolfo Avella, Ferdinando Mancini, Satoru Odashima

Physica C SuperconductivityMay 1, 20034 citations

N=1,

2, 3, and 4 electrons are determined by variational minimization of the sum of the electronic and the phononic energy, paying special attention to the effects of the above-mentioned phonon-induced long-range interaction. To characterize the physics of each ground state, we evaluate how variations of the site spacing affect the behavior of several correlation functions of experimental interest, with the aim of representing lattice deformation effects, either spontaneous or induced by external pressure.