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Physical review. B, Condensed matter

Two-dimensional Hubbard-Holstein model

Elke Berger, P. Valášek, Wolfgang von der Linden

Published Aug 15, 1995• 99 citations
Publisher

Abstract

The interplay of electron-phonon coupling and strong electronic correlations is studied in the frame of the two-dimensional Hubbard-Holstein model. Static and dynamic properties are determined by quantum Monte Carlo simulations and by Migdal-Eliashberg theory. The comparison allows us to assess the diagrammatic approach. The competition between the phonon-mediated electron-electron attraction and the local Coulomb repulsion leads to a rich phase diagram, which we study in detail for a wide range of parameters. We address the question, to which extent the systems can be described by an effective negative-U Hubbard model.

DOI
10.1103/physrevb.52.4806

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The interplay of electron-phonon coupling and strong electronic correlations is studied in the frame of the two-dimensional Hubbard-Holstein model. Static and dynamic properties are determined by quantum Monte Carlo simulations and by Migdal-Eliashberg theory. The comparison allows us to assess the diagrammatic approach. The competition between the phonon-mediated electron-electron attraction and the local Coulomb repulsion leads to a rich phase diagram, which we study in detail for a wide range of parameters. We address the question, to which extent the systems can be described by an effective negative-U Hubbard model.
Abstract The electron–electron and electron–phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
We study the Holstein-Hubbard model at half filling to explore ordered phases including superconductivity (SC), antiferromagnetism (AF), and charge order (CO) in situations where the electron-electron and electron-phonon interactions are strong (comparable to the electronic bandwidth). The model is solved in the dynamical mean-field approximation with a continuous-time quantum Monte Carlo impurity solver. We determine the superconducting transition temperature Tc{T}_{c}Tc​ and the SC order parameter and show that the phonon-induced retardation or the strong Coulomb interaction leads to a significant reduction and shift of the Tc{T}_{c}Tc​ dome against the effective electron-electron interaction Ueff{U}_{\text{eff}}Ueff​ given by the Hubbard UUU reduced by the phonon-mediated attraction in the static limit. This behavior is analyzed by comparison to an effective static model in the polaron representation with a renormalized bandwidth. In addition, we discuss the superconducting gap $\ensuremath{\Delta}$ and $2\ensuremath{\Delta}/{T}_{c}$ to reveal the effect of the retardation and the Coulomb interaction. We also determine the finite-temperature phase diagram including AF and CO. In the moderate-coupling regime, there is a hysteretic region of AF and CO around Ueff=0{U}_{\mathrm{eff}}=0Ueff​=0, while the two phases are separated by a paramagnetic metal in the weak-coupling regime and a paramagnetic insulator in the strong-coupling regime.
Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of sss-wave pairing between charge and magnetic orders
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) sss-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion UUU and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large UUU at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and UUU. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and∕or electron-electron interaction.
We investigate the interaction of strongly correlated electrons with phonons in the frame of the Hubbard-Holstein model. The electron-phonon interaction is considered to be strong and is an important parameter of the model besides the Coulomb repulsion of electrons and band filling. This interaction with the nondispersive optical phonons has been transformed to the problem of mobile polarons by using the canonical transformation of Lang and Firsov. A new diagram technique is used in order to handle the strong Coulomb repulsion of the electrons, which leads to a closed set of integral equations for the irreducible on-site many-particle Green's functions. The coupling to the phonons leads to an essential renormalization of the one- and two-particle irreducible Green's functions. It also influences the parameters which control the metal-insulator or superconducting phase transition. In addition we find a collective mode of phonon clouds which surround the polarons. The physics of the emission and absorption of this mode by the polarons has been investigated.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.