Hubbard Model with superconductivity aspects

The bilayer Hubbard model with an intralayer hopping $t$ and an interlayer hopping ${t}_{\ensuremath{\perp}}$ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half filling, if the splitting between the bonding and antibonding bands ${t}_{\ensuremath{\perp}}/t$ is small, the gap has ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave) symmetry, but when the splitting becomes larger, ${A}_{1g}$ (${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave) pairing is favored. We also find that in the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing region, the pairing is driven by interlayer spin fluctuations and that ${T}_{c}$ is enhanced.The bilayer Hubbard model with an intralayer hopping $t$ and an interlayer hopping ${t}_{\ensuremath{\perp}}$ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half filling, if the splitting between the bonding and antibonding bands ${t}_{\ensuremath{\perp}}/t$ is small, the gap has ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave) symmetry, but when the splitting becomes larger, ${A}_{1g}$ (${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave) pairing is favored. We also find that in the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing region, the pairing is driven by interlayer spin fluctuations and that ${T}_{c}$ is enhanced.

Physical Review BNov 28, 201183 citations

Pairing correlations in the cuprates: A numerical study of the three-band Hubbard model

Peizhi Mai, Giovanni Balduzzi, Steven Johnston +1 more

We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an ``optimal'' value of the charge-transfer energy for the model where ${T}_{c}$ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an ``optimal'' value of the charge-transfer energy for the model where ${T}_{c}$ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.

arXiv:2101.10965Physical review. B./Physical review. BApr 19, 202124 citations

Superconductivity in the Hubbard-Holstein model

Hiroki Goto, Takashi Hotta, Yasutami Takada +3 more

Jan 1, 19950 citations

Resurgence and renormalons in the one-dimensional Hubbard model

Marcos Mariño, Tomás Reis

We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.

arXiv:2006.05131SciPost PhysicsNov 22, 202216 citations

SUPERCONDUCTING STATE IN THE HUBBARD MODEL

A. N. Bogolyubov, А. В. Москаленко

Soviet physics. DokladyFeb 1, 19910 citations

The bilayer Hubbard model with an intralayer hopping

t

and an interlayer hopping ${t}_{\ensuremath{\perp}}$ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half filling, if the splitting between the bonding and antibonding bands ${t}_{\ensuremath{\perp}}/t$ is small, the gap has

{B}_{1g}

(${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave) symmetry, but when the splitting becomes larger,

{A}_{1g}

(${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave) pairing is favored. We also find that in the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing region, the pairing is driven by interlayer spin fluctuations and that

{T}_{c}

is enhanced.

{T}_{c}

is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.