Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

Abstract

We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the nonequilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the nonequilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block-decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines the so-called optimal phonon modes. We discuss their structure in nonequilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.

Photoinduced charge-order melting dynamics in a one-dimensional interacting Holstein model

“…43,[50][51][52][53] The wave function is represented as the matrix-product state form as |Ψ = σ1,σ2,...…”

Dynamics of screening in photodoped Mott insulators

“…[31] showed that for weak nearest-neighbor interaction V the integral over the bosonic Weiss field scales as dωIm[D(ω)] ∝ V 2 . Hence our phenomenological analysis shows that the enhancement of the relaxation due to the nonlocal interaction V and the corresponding V 2 scaling is consistent with a relaxation aided by the coupling to a bath of bosonic degrees of freedom (plasmons) [36,[43][44][45][46].…”

Coexistence of excited polarons and metastable delocalized states in photoinduced metals

“…Note added in proof: We would like to mention the recent publication of work by Dorfner et al [49], providing a comprehensive analysis of the single-electron Holstein mode in one dimension. Although the main focus of this paper is not in the adiabatic regime, the results for the weak-coupling regime are in agreement with our discussion.…”