Retardation effects in the Holstein-Hubbard chain at half-filling

Abstract

The ground state phase diagram of the half-filled one-dimensional Holstein-Hubbard model contains a charge-density-wave (CDW) phase, driven by the electron-phonon (e-ph) coupling, and a spin-density-wave (SDW) phase, driven by the on-site electron-electron (e-e) repulsion. Recently, the existence of a third phase, which is metallic and lies in a finite region of parameter space between these two gapped phases, has been claimed. We study this claim using a renormalization-group method for interacting electrons that has been extended to include also e-ph couplings. Our method treats e-e and e-ph interactions on an equal footing and takes retardation effects fully into account. We find a direct transition between the spin- and charge-density wave states. We study the effects of retardation, which are particularly important near the transition, and find that Umklapp processes at finite frequencies drive the CDW instability close to the transition. We also perform determinantal quantum Monte Carlo calculations of correlation functions to confirm our results for the phase diagram.

4 pages

References in corpus (3)

• Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators
• Renormalization Group Approach to Strong-Coupled Superconductors
• Phase diagram and isotope effects of the quasi-one-dimensional electron gas coupled to phonons

Cited by in corpus (13)

• Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
• Phase diagram of the one dimensional Hubbard-Holstein Model at 1/2 and 1/4 filling
• Competition between antiferromagnetic and charge order in the Hubbard-Holstein model
• Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
• Retardation effects and the Coulomb pseudopotential in the theory of superconductivity
• The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method
• Nature of ground states in one-dimensional electron-phonon Hubbard models at half-filling
• Role of electron-phonon interaction in a magnetically driven mechanism for superconductivity
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model
• Tuning competition between charge order and superconductivity in the square-lattice $t$-$t^{\prime }$-$J$ model
• Nonadiabatic Fluctuations and the Charge-Density-Wave Transition in One-Dimensional Electron-Phonon Systems: a Dynamic Self-Consistent
• Renormalization group approach to anisotropic superconductivity