Metallicity in the half-filled Holstein-Hubbard model

We re-examine the Peierls insulator to Mott insulator transition scenario in the one-dimensional Holstein-Hubbard model where, at half-filling, electron-phonon and electron-electron interactions compete for establishing chargeand spin-density-wave states, respectively. By means of large-scale density-matrix renormalization group calculations we determine the spin, single-particle and two-particle excitation gaps and prove—in the course of a careful finite-size scaling analysis—recent claims for an intervening metallic phase in the weak-coupling regime. We show that for large phonon frequencies the metallic region is even more extended than previously expected, and subdivided into ordinary Luttinger liquid and bipolaronic liquid phases. The challenge of understanding the subtle interplay of electron-electron and electron-phonon interaction effects in low-dimensional condensed matter systems, such as conjugated polymers, charge transfer salts, inorganic spin-Peierls compounds, halogen-bridged transition metal complexes, ferroelectric perovskites, or organic superconductors, [1–4] has stimulated intense work on generic fermion/spin-boson models. In this respect the one-dimensional (1D) Holstein1-Hubbard2 model (HHM) is particularly rewarding to study. [5–14] It accounts for a tight-binding electron band, an intra-site Coulomb repulsion between electrons of opposite spin, a local coupling of the charge carriers to optical phonons, and the energy of the phonon subsystem in harmonic approximation: