We study the Hubbard-Holstein model which includes both the electron-electron and electron-phonon interactions, characterized by
U and
g, respectively. The model is solved with
U and
g 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
U and
g are small, but is insulating when
U or
g 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
z 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.
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.
Abstract We explore the quantum phase transitions between two ordered states in the infinite dimensional Hubbard–Holstein model at half filling. Our study is based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG), which allows us to handle both strong electron–electron and strong electron–phonon interactions. The transition line is characterized by an effective electron–electron interaction. Depending on this effective interaction and the phonon frequency ω0 one finds either a continuous transition or discontinuous transition. Here, the analysis focuses on the behavior of the system when the electron–electron repulsion U and the phonon‐mediated attraction λ are equal. We first discuss the adiabatic and antiadiabatic limiting cases. For finite ω0 we study the differences between the antiferromagnetic (AFM) and charge order, and find that when present the AFM state has a lower energy on the line.