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

Abstract

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.

Fermi-surface-induced lattice distortion inNbTe2

“…Within the Fermiliquid picture, ARPES peaks are attributed to quasiparticle excitations, whose lifetime increases when approaching the Fermi level. This procedure is well justified by recent theoretical calculations of the spectral function for the spinless Holstein model in the weak coupling regime [44,45]. In contrast in the strong coupling regime, the coherent quasiparticle band flattens considerably and possesses exponentially small spectral weight [44,45].…”

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

“…Here, we extend our recent work [21] on the one-dimensional spinless Holstein model (1) where the scope of this paper is twofold: Firstly, we demonstrate that the PRM approach of Ref. [21] is not restricted to the half-filled case, and that the phonon dispersion relation close to the critical value of the EP coupling reflects the type of the broken symmetry of the insulating phase.…”

“…Recently, we applied the projector-based renormalization method (PRM) [18] to the spinless Holstein model (1) at half-filling [21]. This analytical approach does not suffer from the truncation of the phononic Hilbert space so that all bosonic degrees of freedom are taken into account.…”

Lang-Firsov Approaches to Polaron Physics: From Variational Methods to Unbiased Quantum Monte Carlo Simulations

“…These peaks-not present at T = 0 [50,51]-arise from thermally activated transitions to states with additional phonons excited, and are also visible in figures 11 and 13. While for WC (λ = 0.1, figure 11), the maximum of these features is almost exactly located at |ω − µ| = ω 0 , it moves to |ω − µ| ≈ 1.25ω 0 for IC (λ = 1, figure 15), and finally to |ω − µ| ≈ 2.5ω 0 for SC (λ = 2, figure 13).…”