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.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.

Physical review. B, Condensed matterAug 15, 199599 citations

Excitation spectrum of the two-dimensional attractive Hubbard model

Massimiliano Capezzali, Hans Beck

arXiv:cond-mat/9809349Physica C SuperconductivityMay 1, 19993 citations

Half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations

Sebastião dos Anjos Sousa-Júnior, Natanael C. Costa, Raimundo R. dos Santos

The extended Hubbard model describes fermions on a lattice coupled through on-site, $U$ , and first-neighbor, $V$ , interactions. In the context of high- ${T}_{c}$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered, $s$ - and $d$ -wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram, ${T}_{c}(U,V)$ , featuring critical temperatures for the charge-density wave and $s$ -wave superconducting phases.The extended Hubbard model describes fermions on a lattice coupled through on-site, $U$, and first-neighbor, $V$, interactions. In the context of high-${T}_{c}$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered, $s$- and $d$-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram, ${T}_{c}(U,V)$, featuring critical temperatures for the charge-density wave and $s$-wave superconducting phases.

arXiv:2304.08683Physical review. B./Physical review. BApr 1, 202415 citations

Spectral properties of the attractive Hubbard model

Martin Letz, R.J. Gooding

arXiv:cond-mat/9802110Journal of Physics and Chemistry of SolidsOct 1, 19982 citations

Quantum Monte Carlo study of the three-dimensional attractive Hubbard model

Alain Sewer, X. Zotos, Hans Beck

We study the three-dimensional (3D) attractive Hubbard model by means of the determinant quantum Monte Carlo method. This model is a prototype for the description of the smooth crossover between BCS superconductivity and Bose-Einstein condensation. By detailed finite-size scaling we extract the finite-temperature phase diagram of the model. In particular, we interpret the observed behavior according to a scenario of two fundamental temperature scales; ${T}^{*}$ associated with Cooper pair formation and ${T}_{c}$ with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high- ${T}_{c}$ cuprate superconductors.We study the three-dimensional (3D) attractive Hubbard model by means of the determinant quantum Monte Carlo method. This model is a prototype for the description of the smooth crossover between BCS superconductivity and Bose-Einstein condensation. By detailed finite-size scaling we extract the finite-temperature phase diagram of the model. In particular, we interpret the observed behavior according to a scenario of two fundamental temperature scales; ${T}^{*}$ associated with Cooper pair formation and ${T}_{c}$ with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high-${T}_{c}$ cuprate superconductors.

arXiv:cond-mat/0204053Physical review. B, Condensed matterOct 9, 200239 citations

The extended Hubbard model describes fermions on a lattice coupled through on-site,

U

, and first-neighbor,

V

, interactions. In the context of high-

{T}_{c}

cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered,

s

- and

d

-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram,

{T}_{c}(U,V)

, featuring critical temperatures for the charge-density wave and

s

-wave superconducting phases.

{T}^{*}

associated with Cooper pair formation and

{T}_{c}

with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high-

{T}_{c}

cuprate superconductors.