One-dimensional Spinless Holstein Model Research Articles

Electron addition spectral functions of low-density polaron liquids

Spectral functions are important quantities that contain a wealth of information about the quasiparticles of a system, and that can also be measured experimentally. For systems with electron-phonon coupling, good approximations for the spectral function are available only in the Migdal limit (at Fermi energies much larger than the typical phonon frequency, E_F\gg \OmegaEF≫Ω, requiring a large carrier concentration xx) and in the single polaron limit (at x=0x=0). Here we show that the region with x\ll 1x≪1(E_F<\OmegaEF<Ω) can also be reliably investigated with the Momentum Average (MA) variational approximation, which essentially describes the formation of a polaron above an inert Fermi sea. Specifically, we show that for the one-dimensional spinless Holstein model, the MA spectral functions compare favorably with those calculated using variationally exact density matrix renormalization group simulations (DMRG) evaluated directly in frequency-space, so long as x<0.1x<0.1 and the adiabaticity ratio \Omega/t>0.5Ω/t>0.5. Unlike in the Migdal limit, here 'polaronic physics’ emerges already at moderate couplings. The relevance of these results for a spinful low-xx metal is also discussed.

Dynamic charge correlations near the Peierls transition

The quantum phase transition between a repulsive Luttinger liquid and an insulating Peierls state is studied in the framework of the one-dimensional spinless Holstein model. We focus on the adiabatic regime but include the full quantum dynamics of the phonons. Using continuous-time quantum Monte Carlo simulations, we track in particular the dynamic charge structure factor and the single-particle spectrum across the transition. With increasing electron-phonon coupling, the dynamic charge structure factor reveals the emergence of a charge gap, and a clear signature of phonon softening at the zone boundary. The single-particle spectral function evolves continuously across the transition. Hybridization of the charge and phonon modes of the Luttinger liquid description leads to two modes, one of which corresponds to the coherent polaron band. This band acquires a gap upon entering the Peierls phase, whereas the other mode constitutes the incoherent, high-energy spectrum with backfolded shadow bands. Coherent polaronic motion is a direct consequence of quantum lattice fluctuations. In the strong-coupling regime, the spectrum is described by the static, mean-field limit. Importantly, whereas finite electron density in general leads to screening of polaron effects, the latter reappear at half filling due to charge ordering and lattice dimerization.

Optical conductivity of polaronic charge carriers

The optical conductivity of charge carriers coupled to quantum phonons is studied in theframework of the one-dimensional spinless Holstein model. For one electron, variationaldiagonalization yields exact results in the thermodynamic limit, whereas at finite carrierdensity analytical approximations based on previous work on single-particle spectralfunctions are obtained. Particular emphasis is put on deviations from weak-coupling,small-polaron or one-electron theories occurring at intermediate coupling and/or finitecarrier density. The analytical results are in surprisingly good agreement with exact data,and exhibit the characteristic polaronic excitations observed in experiments on manganites.

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

We study the one-dimensional Holstein model of spinless fermions interacting with dispersion-less phonons by using a recently developed projector-based renormalization method (PRM). At half-filling the system shows a metal-insulator transition to a Peierls distorted state at a critical electron-phonon coupling where both phases are described within the same theoretical framework. The transition is accompanied by a phonon softening at the Brillouin zone boundary and a gap in the electronic spectrum. For different filling, the phonon softening appears away from the Brillouin zone boundary and thus reflects a different type of broken symmetry state.

Spectral functions of the spinless Holstein model

An analytical approach to the one-dimensional spinless Holstein model is proposed, whichis valid at finite charge-carrier concentrations. Spectral functions of charge carriers arecomputed on the basis of self-energy calculations. A generalization of the Lang–Firsovcanonical transformation method is shown to provide an interpolation scheme between theextreme weak-coupling and strong-coupling cases. The transformation depends on avariationally determined parameter that characterizes the charge distribution across thepolaron volume. The relation between the spectral functions of the polaron and electron,the latter corresponding to the photoemission spectrum, is derived. Particular attention ispaid to the distinction between the coherent and incoherent parts of the spectra, and theirevolution as a function of band filling and model parameters. Results are discussedand compared with recent numerical calculations for the many-polaron problem.

Photoemission spectra of many-polaron systems

The crossover from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points toward the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.

Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model

We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both approaches. Moreover, the PRM approach reveals the softening of a phonon at the Brillouin-zone boundary which can be understood as precursor effect of the gap formation.

Nonlinear Lattice Effect on Ground State of One-Dimensional Electron-Phonon System**The project supported by the Research Foundation of Hunan Normal University under Grant No.200606

We study the nonlinear lattice effect on the ground state in a one-dimensional spinless Holstein model with nonadiabitical coupling and squeezing by means of the parameter variational approach. Our results show that the introduction of a hard quartic term in the lattice potential increases the ground state energy of the system when electron-phonon coupling is strong, and the increment is sensitive to the magnitude of the lattice quartic force constant. In this case the nonlinear lattice effects should be taken into account to describe satisfactorily some physical properties of the coupling system.

Phase diagram and optical conductivity of the one-dimensional spinless Holstein model

The effects of quantum lattice fluctuations on the Peierls transition and the optical conductivity in the one-dimensional Holstein model of spinless fermions have been studied by developing an analytical approach, based on the unitary transformation method. We show that when the electron-phonon coupling constant decreases to a finite critical value the Peierls dimerization is destroyed by the quantum lattice fluctuations. The dimerization gap is much more reduced by the quantum lattice fluctuations than the phonon order parameter. The calculated optical conductivity does not have the inverse-square-root singularity but have a peak above the gap edge and there exists a significant tail below the peak. The peak of optical-conductivity spectrum is not directly corresponding to the dimerized gap. Our results of the phase diagram and the spectral-weight function agree with those of the density matrix renormalization group and the exact diagonalization methods.

Gapped and gapless ground state of the one-dimensional spinless Holstein model

An analytical approach has been developed to study the ground-state phase diagram of a one-dimensional spinless Holstein model and its gapped and gapless phases. We show that when the electron-phonon coupling constant ${g}^{2}/{\ensuremath{\omega}}_{0}$ decreases or the phonon frequency ${\ensuremath{\omega}}_{0}$ increases the lattice dimerization and the gap in the fermionic spectrum decreases gradually. At some critical value ${(g}^{2}/{\ensuremath{\omega}}_{0}{)}_{c}$ or ${\ensuremath{\omega}}_{0c},$ the lattice dimerization disappears and the system becomes gapless Luttinger liquid with phonon-renormalized velocity $v(q)$ and stiffness constant $K(q).$ Our numerical results agree quite well with the results of Monte Carlo simulations.