Ka-Ming Tam

Retardation effects in the Holstein-Hubbard chain at half filling

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 [Tsai et al., Phys. Rev. B 72, 054531 (2005); Philos. Mag. B 86, 2631 (2006)] 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 SDW and CDW 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.

Phase diagram of the Holstein-Hubbard two-leg ladder using a functional renormalization-group method

Using a functional renormalization-group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization-group technique allows us to analyze the problem for both weak and strong electron-phonon couplings. We show that, in contrast to results from conventional weak-coupling studies, electron-phonon interactions can dominate electron-electron interactions, and retardation effects play an important role on the phase diagram.

Dominant superconducting fluctuations in the one-dimensional extended Holstein-extended Hubbard model

Author(s): Tam, KM; Tsai, SW; Campbell, DK | Abstract: The search for realistic one-dimensional (1D) models that exhibit dominant superconducting (SC) fluctuations effects has a long history. In these 1D systems, the effects of commensurate band fillings - strongest at half-filling - and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. Accordingly, recent proposals suggesting a gapless metallic state in the Holstein-Hubbard (HH) model, possibly superconducting, have generated considerable interest and controversy, with the most recent work demonstrating that the putative dominant superconducting state likely does not exist. In this paper we study a model with nonlocal electron-phonon interactions, in addition to electron-electron interactions. This model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using both the numerical multi-scale functional renormalization group (MFRG) for the full model and an analytic conventional renormalization group for a bosonized version of the model, we demonstrate the existence of these dominant SC fluctuations and show that they arise because the spin-charge coupling at high energies is weakened by the nonlocal electron-phonon interaction and the charge gap is destroyed by the resultant suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that nonlocal boson-mediated interactions may be important in the superconductivity observed in the organic superconductors.

Validity of the Tomonaga Luttinger liquid relations for the one-dimensional Holstein model

Author(s): Tam, KM; Tsai, SW; Campbell, DK | Abstract: For the one-dimensional Holstein model, we show that the relations among the scaling exponents of various correlation functions of the Tomonaga Luttinger liquid (LL), while valid in the thermodynamic limit, are significantly modified by finite-size corrections. We obtain analytical expressions for these corrections and find that they decrease very slowly with increasing system size. The interpretation of numerical data on finite-size lattices in terms of LL theory must therefore take these corrections into account. As an important example, we re-examine the proposed metallic phase of the zero-temperature, half-filled one-dimensional Holstein model without employing the LL relations. In particular, using quantum Monte Carlo calculations, we study the competition between the singlet pairing and charge ordering. Our results do not support the existence of a dominant singlet pairing state.