Emergence of states in the phonon spectral function of the Holstein polaron below and above the one-phonon continuum

TL;DR

This paper explores the low-energy excitations of the Holstein polaron by calculating the phonon spectral function, revealing new bound and antibound states influenced by electron-phonon interactions, using advanced numerical techniques.

Contribution

It introduces an improved exact-diagonalization method to study the phonon spectral function, uncovering novel bound and antibound states across different coupling regimes.

Findings

Identification of bound and antibound states in the phonon spectral function.

Good agreement between numerical results and strong-coupling perturbation theory.

Observation of these states below and above the one-phonon continuum.

Abstract

We investigate the low-energy properties of the Holstein polaron through calculation of the q-dependent phonon spectral function using an improved exact-diagonalization technique, defined over a variational Hilbert space. We perform a comprehensive study of the low-energy excitations of the polaron. Beside the energy range, where the additional phonon excitation is unbound, we observe separate coherent peaks which correspond to bound and antibound states of a polaron and additional phonon quanta. These novel states can be observed for intermediate and strong electron-phonon coupling strengths, as well as below and above the unbound one-phonon excitation spectrum. A detailed investigation of their properties is presented. We find good agreement between the phonon spectral function obtained from the first-order strong-coupling perturbation theory and numerical results.