Metallicity in the half-filled Holstein-Hubbard model

Abstract

Abstract. -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 charge-and 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][2][3][4] has stimulated intense work on generic fermion/spin-boson models. In this respect the one-dimensional (1D) Holstein 1 -Hubbard 2 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: The physics of the HHM is governed by three competing effects: the itinerancy of the electrons (∝ t), their onsite Coulomb repulsion (∝ U ), and the local electron-phonon (EP) coupling (∝ ε p ). Since the EP interaction is retarded, the phonon frequency (ω 0 ) defines a further relevant energy scale. Hence one is advised to introduce besides the adiabaticity ratio,two dimensionless coupling constants:Both Holstein and Hubbard interactions tend to immobilize the charge carriers, and even may drive a metal-insulator transition at commensurate band fillings. For the half-filled band case (one electron per lattice site), most previous analytical and numerical studies of the HHM reveal that Peierls insulator (PI) or Mott insulator (MI) states are favored over the metallic state at zero temperature. Whereas the PI is characterized by a distortion of the underlying lattice accompanied by dominant charge-density-wave (CDW) correlations, the Mott insulator is basically a spin-density-wave (SDW) state without any lattice dimerization. The physical excitations differ accordingly: while "normal" electron-hole excitations are expected in

Competition Between Antiferromagnetic and Charge-Density-Wave Order in the Half-Filled Hubbard-Holstein Model

“…The U -λ phase diagram determined in our study is qualitatively similar to that found by low temperature numerical approaches, with the U eff =0 line dividing the regions of dominant spin and charge order parameters. We found evidence for an intermediate metallic phase in two dimensions, similar to previous 1-d results.. [14][15][16][17] The size of the intermediate metallic region shrinks as the interaction strengths grow, which is consistent with Refs. 15-17 where the metallic phase is found to terminate at strong couplings.…”

“…In one dimension, the HH phase diagram has been established via several numerical approaches, with an intermediate metallic state between the AFM and CDW phases. [14][15][16][17][18] The size of the metallic region grows with increasing phonon frequency. [15][16][17] A similar competition between AFM and CDW orders and phase diagram have been mapped out in infinite dimensions with DMFT.…”

“…[14][15][16][17][18] The size of the metallic region grows with increasing phonon frequency. [15][16][17] A similar competition between AFM and CDW orders and phase diagram have been mapped out in infinite dimensions with DMFT. [19][20][21][22][23] The AFM-CDW competition in two dimensions also has arXiv:1209.0829v1 [cond-mat.str-el] 4 Sep 2012 been studied with perturbative 24,25 as well as strong coupling 26 techniques.…”

Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

“…The spin gap is a result of backscattering. Signatures of this LutherEmery phase have also been observed in the Holstein-Hubbard model with comparable electron-phonon and electron-electron interactions [38,18,19,22,23]. Our results presented below suggest that in contrast to half filling, we can observe dominant pairing correlations for high phonon frequencies at a commensurate density; dominant pairing for incommensurate filling has been reported before [39].…”

Spin density waves predicted in zigzag puckered phosphorene, arsenene and antimonene nanoribbons

“…We usually notice the ratio between U and t (U/t), since SDW order depends on U/t. 29,30 The increasing of positive strains leads to the reducing of the neighbor hopping t, but on-site U just changes little, which indicates positive strains will increase the value of U/t. Accordingly, positive strains can increase the SDW magnetic moments and band gaps, while electrons become more and more localized.…”