Isotope effects in the Hubbard-Holstein model within dynamical mean-field theory

Abstract

We study the isotope effects arising from the coupling of correlated electrons with dispersionless phonons by considering the Hubbard-Holstein model at half-filling within the dynamical mean-field theory. In particular we calculate the isotope effects on the quasi-particle spectral weight $Z$, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime $U/t\lesssim 1.5$, where $U$ is the Hubbard repulsion and $t$ is the bare electron half-bandwidth, the physical properties are qualitatively similar to those characterizing the Holstein model in the absence of Coulomb repulsion, where the bipolaronic binding takes place at large electron-phonon coupling, and it reflects in divergent isotope responses. On the contrary in the strongly correlated regime $U/t\gtrsim 1.5$, where the bipolaronic metal-insulator transition becomes of first order, the isotope effects are bounded, suggesting that the first order transition is likely driven by an electronic mechanism, rather then by a lattice instability. These results point out how the isotope responses are extremely sensitive to phase boundaries and they may be used to characterize the competition between the electron-phonon coupling and the Hubbard repulsion.

arXiv comment10 pages, 8 figures. The paper has been already accepted on Phys. Rev. B

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• Gutzwiller scheme for electrons and phonons: the half-filled Hubbard-Holstein model
• First Order Bipolaronic Transition at Finite Temperature in the Holstein Model
• Repulsive vs. attractive Hubbard model: transport properties and spin-lattice relaxation rate
• Kink structure in the electronic dispersion of high-Tc superconductors from the electron-phonon interaction
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• Next-generation EDIpack: A Lanczos-based package for quantum impurity models featuring general broken-symmetry phases, flexible bath topologies and multi-platform interoperability
• Metal-insulator transition and superconductivity in the two-orbital Hubbard-Holstein model for iron-based superconductors
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization