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arXiv:cond-mat/0409510 · Physical Review Letters

Electron-Phonon Interaction Close to a Mott Transition

Giorgio Sangiovanni, Massimo Capone, Claudio Castellani, M. Grilli

Published Jan 18, 2005• 114 citations
arXivHTMLPDF

Abstract

The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half filling is investigated by means of dynamical mean-field theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained interpreting the quasiparticle motion in terms of rare fast processes.

DOI
10.1103/physrevlett.94.026401

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The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half filling is investigated by means of dynamical mean-field theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained interpreting the quasiparticle motion in terms of rare fast processes.
The role of the electron-phonon interaction in the Holstein-Hubbard model is investigated in the metallic phase close to the Mott transition and in the insulating Mott phase. The model is studied by means of a variational slave boson technique. At half-filling, mean-field static quantities are in good agreement with the results obtained by numerical techniques. By taking into account Gaussian fluctuations, an analytic expression of the spectral density is derived in the Mott insulating phase showing that an increase of the electron-phonon coupling leads to a sensitive reduction of the Mott gap through a reduced effective repulsion. The relation of the results with recent experimental observations in strongly correlated systems is discussed.
The properties of the electron-phonon interaction in the presence of a sizable electronic repulsion at finite doping are studied by investigating the metallic phase of the Hubbard-Holstein model with dynamical mean-field theory. Analyzing the quasiparticle weight at finite doping, we find that a large Coulomb repulsion reduces the effect of electron-phonon coupling at low energy, while this reduction is not present at high energy. The renormalization of the electron-phonon coupling induced by the Hubbard repulsion depends in a surprisingly strong and nontrivial way on the phonon frequency. Our results suggest that phonon might affect differently high-energy and low-energy properties and this, together with the effect of phonon dynamics, should be carefully taken into account when the effects of the electron-phonon interaction in a strongly correlated system, like the superconducting cuprates, are discussed.
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 quasiparticle spectral weight ZZZ, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime $U∕t\ensuremath{\lesssim}1.5$, where UUU is the Hubbard repulsion and ttt 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 is reflected in divergent isotope responses. On the contrary in the strongly correlated regime $U∕t\ensuremath{\gtrsim}1.5$, 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.
We study the Hubbard-Holstein model which includes both the electron-electron and electron-phonon interactions, characterized by UUU and ggg, respectively. The model is solved with UUU and ggg on an equal footing in the infinite dimensions by employing the dynamical mean-field theory in combination with Wilson's numerical renormalization group. A zero temperature phase diagram of symmetry unbroken states at half filling is mapped out which exhibits the interplay between the two kinds of interactions and combines the two separately studied interaction-driven metal-insulator transitions of the Hubbard and Holstein models within a single frame. The ground state is metallic when both UUU and ggg are small, but is insulating when UUU or ggg is large, referred to as, respectively, Mott-Hubbard insulator (MHI) and bipolaron insulator (BPI). As the phase boundary between the metallic and MHI (BPI) states is approached from the metallic region, the quasiparticle weight zzz goes to 0 continuously (discontinuously). Moreover, the two insulating states are distinct and cannot be adiabatically connected, and there is a first order phase transition between them.
We present a method for solving impurity models with electron-phonon coupling, which treats the phonons efficiently and without approximations. The algorithm is applied to the Holstein-Hubbard model in the dynamical mean field approximation, where it allows access to strong interactions, very low temperatures, and arbitrary fillings. We show that a renormalized Migdal-Eliashberg theory provides a reasonable description of the phonon contribution to the electronic self-energy in strongly doped systems, but fails if the quasiparticle energy becomes of order of the phonon frequency.
We present results on the dynamical correlation functions of the particle-hole symmetric Holstein-Hubbard model at zero temperature, calculated using the dynamical mean-field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behavior in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propagator shows a characteristic softening near the metal to bipolaronic transition but there is very little softening on the approach to the Mott transition.