Analytical approach to the quantum-phase transition   in the one-dimensional 
 spinless Holstein model

Sykora, Steffen; Hübsch, A.; Becker, K. W.

doi:10.1140/epjb/e2006-00211-1

Cited by 15 publications

(32 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In accordance with the analytical results of Refs. [17,25], a hybridization of the phonon mode with the particle-hole continuum is also visible near q = π , and gives rise to damping of the phonon excitations. The above explanation suggests that the small-q feature is absent deep in the insulating Peierls phase, because the latter does not have low-energy excitations near q = 0.…”

Section: B Origin Of the Small-q Featurementioning

confidence: 98%

“…The phonon spectrum of the 1D, half-filled spinless Holstein model was studied in Refs. [17,19,22,23,25]. Numerical results were obtained using exact diagonalization (restricted to small cluster sizes) [19], cluster perturbation theory (with artifacts related to the inherent translation symmetry breaking) [19], and QMC (restricted in cluster size and temperature, and with a Trotter error) [22].…”

Section: Modelmentioning

confidence: 99%

“…For a single electron, the phonon spectrum can again be calculated to arbitrary precision [24]. The phonon spectral function and the renormalized phonon frequency of the spinless Holstein model were obtained with the projector-based renormalization method [17,23,25]. The electronic spectral function of the Holstein-Hubbard model was calculated to characterize the metallic, Mott, and Peierls phases [26][27][28], and to study the impact of electron-phonon coupling on spin-charge separation [29,30].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phonon spectral function of the one-dimensional Holstein-Hubbard model

2015

View full text Add to dashboard Cite

We use the continuous-time interaction expansion (CT-INT) quantum Monte Carlo method to calculate the phonon spectral function of the one-dimensional Holstein-Hubbard model at half-filling. Our results are consistent with a soft-mode Peierls transition in the adiabatic regime, and the existence of a central peak related to long-range order in the Peierls phase. We explain a previously observed feature at small momenta in terms of a hybridization of charge and phonon excitations. Tuning the system from a Peierls to a metallic phase with a nonzero Hubbard interaction suppresses the central peak, but a significant renormalization of the phonon dispersion remains. In contrast, the dispersion is only weakly modified in the Mott phase. We discuss finite-size effects, the relation to the dynamic charge structure factor, as well as additional sum rules and their implications. Finally, we reveal the existence of a discrete symmetry in a continuum field theory of the Holstein model, which is spontaneously broken in the Peierls phase.Comment: 10 pages, 4 figure

show abstract

Section: B Origin Of the Small-q Featurementioning

confidence: 98%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Phonon spectral function of the one-dimensional Holstein-Hubbard model

2015

View full text Add to dashboard Cite

show abstract

“…Examples are the investigation of phonon-mediated superconductivity starting from an explicit expression for the electron-phonon interaction 30 and the discussion of the metal-insulator transition in the Holstein model. 31 Many-particle systems in the presence of strong correlations such as the PAM were also investigated. 32 In contrast to the slave-boson mean-field treatment, 33 the PRM maps the periodic Anderson model onto an effective model of two independent subsystems of renormalized conduction and f electrons, thereby still taking into account the strong correlations between the localized f electrons.…”

Section: Projector-based Renormalization Methodsmentioning

confidence: 99%

“…This allows a unified treatment of quantum phase transition on both sides of a critical point. 31 In the present investigation an extension of the PRM to continuous transformations will be used which is the better choice for the periodic Anderson model.…”

Section: ͑17͒mentioning

confidence: 99%

Extended periodic Anderson model close to a valence transition: A projector-based renormalization approach

2010

View full text Add to dashboard Cite

The one-dimensional periodic Anderson model with an additional Coulomb repulsion U fc between localized f and conduction electrons has been investigated using the projector-based renormalization method. Due to the presence of U fc and the hybridization V between localized and conduction electrons, various gaps are found in the quasiparticle dispersion k . The number of gaps depends on the density of the localized electrons. Moreover, a valence transition from an integer to a mixed f valence is found as a function of the bare f level energy f . Its dependence on various model parameters is investigated for fixed total electron density. In particular, the transition is sharpened either by increasing U fc or by decreasing the hybridization or the temperature.

show abstract

Phonon spectral function of the Holstein polaron

Loos¹,

Hohenadler²,

Alvermann³

et al. 2006

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Abstract. The phonon spectral function of the one-dimensional, single-electron Holstein model is obtained within weak-and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid on the different physics occurring in the adiabatic and non-adiabatic regimes, respectively. Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit. This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.

show abstract

Analytical approach to the quantum-phase transition in the one-dimensional spinless Holstein model

Cited by 15 publications

References 26 publications

Phonon spectral function of the one-dimensional Holstein-Hubbard model

Phonon spectral function of the one-dimensional Holstein-Hubbard model

Extended periodic Anderson model close to a valence transition: A projector-based renormalization approach

Phonon spectral function of the Holstein polaron

Contact Info

Product

Resources

About