Possibility of a metallic phase in the charge-density-wave–spin-density-wave crossover region in the one-dimensional Hubbard-Holstein model at half filling

Takada, Yogo; Chatterjee, Ashok

doi:10.1103/physrevb.67.081102

Cited by 81 publications

(97 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10,11 The variational results of Ref. 15 find the intermediate phase existing in a narrow region on both sides of the U eff = 0 line, while we find the intermediate phase only for U eff Ͻ 0. Several calculations of the single-particle spectral function are available for the HHM, [41][42][43] the spinless Holstein model, 44,45 as well as the d = ϱ studies previously mentioned.…”

Section: Discussionmentioning

confidence: 77%

“…14 Given that in the half-filled 1D HHM at U = 0 the ground state is metallic ͑no charge gap and a finite Drude weight͒ for a finite value of g, it was proposed that this metallic phase continues to exist between the Peierls and Mott insulating phases for U Ͼ 0. 15 Subsequent numerical calculations confirmed that a metallic phase exists for both U = 0 and finite U. 16 In this paper, we present more detailed numerical results and analysis of the phase diagram.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

2007

View full text Add to dashboard Cite

The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electronphonon interactions. In one dimension at half filling, the Holstein electron-phonon coupling promotes on-site pairs of electrons and a Peierls charge-density wave, while the Hubbard on-site Coulomb repulsion U promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that ͑i͒ as the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions, the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-U Hubbard model.

show abstract

Section: Discussionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

2007

View full text Add to dashboard Cite

show abstract

“…An intervening metallic phase would of course prevent a direct insulator-to-insulator transition. Recent numerical investigations of the 1D HHM, based on variable-displacement LangFirsov [6], DMRG [9,11], and SSE QMC [8,12] approaches, give strong evidence that the CDW-SDW transition does indeed split into two subsequent CDW-metal and metal-SDW transitions in the weak-coupling intermediate-to-large phononfrequency regime. 4 To map out the phase diagram is technically challenging, however, since the energy scales are not well 3 The metal-insulator transition at gc is expected to be of KosterlitzThouless type, at least for ω 0 → ∞ (cf.…”

mentioning

confidence: 99%

“…In this respect the one-dimensional (1D) Holstein 1 -Hubbard 2 model (HHM) is particularly rewarding to study. [5][6][7][8][9][10][11][12][13][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: 343 (1959)) has been studied extensively as a paradigmatic model for polaron formation in the low-density limit. For commensurate band fillings the coupling to the lattice supports charge ordering.…”

mentioning

confidence: 99%

Metallicity in the half-filled Holstein-Hubbard model

2008

View full text Add to dashboard Cite

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

show abstract

“…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.…”

mentioning

confidence: 99%

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

et al. 2012

View full text Add to dashboard Cite

We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge density wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order, so that CDW order remains absent even when the effective U is negative. This delay opens a window where neither AFM nor CDW order is well established, and where there are signatures of a possible metallic phase.PACS numbers: 71.10. Fd, 71.30.+h, 71.45.Lr, The electron-phonon (el-ph) interaction is responsible for many phenomena in condensed matter physics, including charge density waves (CDWs) and conventional superconductivity. While the el-ph interaction is well understood in metals, the role of phonons in strongly correlated systems is less clear, in part because the interplay of strong electron-electron (el-el) and el-ph interactions can lead to competing ordered phases. Despite its difficulty, this is an important problem to solve because multiple experimental probes have detected signatures of significant lattice effects in strongly correlated materials. For example, in the cuprate high-temperature superconductors, angle-resolved photoemission spectroscopy (ARPES) has observed "kinks" in the band dispersion, which have been attributed to the el-ph interaction, 1 as well as small polaron formation in undoped Ca 2−x Na x CuOCl 2 . 2,3 Additional evidence for a significant el-ph interaction include strong quasiparticle renormalizations detected by STM, 4 and studies which have qualitatively reproduced optical conductivity peaks by including phonons. 5,6 Besides the cuprates, other materials with both strong el-el and el-ph interactions include the manganites 7 and fullerenes. 8On general grounds, two effects are expected when elph interactions are included in a system with strong el-el repulsion. The first is that the two interactions renormalize each other. The phonons mediate a retarded attractive el-el interaction, thus reducing the effective Coloumb repulsion, while the el-el repulsion suppresses charge fluctuations, and hence the el-ph interaction, which couples to them. The second effect is a reduction in the quasiparticle weight due to additional scattering processes, which at large el-ph couplings can lead to a polaron crossover.A natural model for studying the interplay of the elel and el-ph interactions is the Hubbard-Holstein (HH) model, which has been studied using various numerical approaches producing sometimes contradicting results. Within dynamical mean field theory (DMFT), the suppression of the el-ph interaction depends on the underlying phase, and antiferromagnetic (AFM)-DMFT has found a moderate increase i...

show abstract

Possibility of a metallic phase in the charge-density-wave–spin-density-wave crossover region in the one-dimensional Hubbard-Holstein model at half filling

Cited by 81 publications

References 19 publications

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

Metallicity in the half-filled Holstein-Hubbard model

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

Contact Info

Product

Resources

About