On the self-trapping problem of electrons or excitons in one dimension

TL;DR

This paper provides a comprehensive numerical analysis of the one-dimensional Holstein model, exploring electron self-trapping, polaron states, and phase transitions across different regimes, with results aligning well with existing theories and data.

Contribution

It introduces an efficient variational Lanczos method to analyze ground states and phase diagrams, revealing new insights into polaron states and self-trapping phenomena in one-dimensional systems.

Findings

Complete phase diagram of the Holstein model.

Identification of two types of small polarons in strong coupling.

Observation of a crossover from large to small polarons with spectral changes.

Abstract

We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electrons or excitons in crystals with short-range particle-lattice interactions. Applying a very efficient variational Lanczos method, we are able to analyze the ground-state properties of the system in the weak-- and strong-coupling, adiabatic and non-adiabatic regimes on lattices large enough to eliminate finite-size effects. In particular, we obtain the complete phase diagram and comment on the existence of a critical length for self-trapping in spatially restricted one-dimensional systems. In order to characterize large and small polaron states we calculate self-consistently the lattice distortions and the particle-phonon correlation functions. In the strong-coupling case, two distinct types of small polaron states are shown to be possible according to the relative importance of static displacement field and dynamic polaron effects. Special emphasis is on the intermediate coupling regime, which we also study by means of direct diagonalization preserving the full dynamics and quantum nature of phonons. The crossover from large to small polarons shows up in a strong decrease of the kinetic energy accompanied by a substantial change in the optical absorption spectra. We show that our numerical results in all important limiting cases reveal an excellent agreement with both analytical perturbation theory predictions and very recent density matrix renormalization group data.