Dynamical properties of the one-dimensional Holstein model

TL;DR

This study investigates the spectral and optical properties of the one-dimensional Holstein model across different electron concentrations, revealing smooth crossovers from free electrons to polaronic and charge-density-wave states as electron-phonon coupling increases.

Contribution

It introduces a density matrix approach to efficiently compute spectral functions and analyze phase crossovers in the Holstein model on a small lattice.

Findings

Evidence of a crossover from free electrons to small polarons and bipolarons with increasing coupling.

Observation of a transition from metallic to Peierls charge-density-wave state at half filling.

Drude weight drops sharply indicating insulating behavior in the Peierls phase.

Abstract

The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasi-free electrons to an heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling we observe a crossover from a quasi-free-electron ground state to a quasi-degenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight which is vanishingly small in the Peierls phase.