Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions

Abstract

We apply weak-coupling perturbation theory to the Holstein molecular crystal model in order to compute an electron-phonon correlation function characterizing the shape and size of the polaron lattice distortion in one, two, and three dimensions. This correlation function is computed exactly to leading order in the electron-phonon coupling constant, permitting a complete description of correlations in any dimension for both isotropic and arbitrarily anisotropic cases. Using this exact result, the width of the polaron is characterized along arbitrary directions. The width of the polaron thus determined disagrees in every dimension with some well-known characterizations of polarons, signalling in particular the breakdown of the adiabatic approximation and the characterizations of self-trapping associated with it.

4 Pages, 2 figures

References in corpus (2)

• Density matrix renormalization group study of the polaron problem in the Holstein model
• Polaron band formation in the Holstein model

Cited by in corpus (12)

• Dimensionality effects on the Holstein polaron
• Polarons and slow quantum phonons
• Variational study of the Holstein polaron
• The Self-Trapping Line of the Holstein Molecular Crystal Model in One Dimension
• Towards Outperforming Classical Algorithms with Analog Quantum Simulators
• Effects of dimensionality and anisotropy on the Holstein polaron
• Phase diagram of the Holstein polaron in one dimension
• Solution of the Holstein polaron anisotropy problem
• Electron-Phonon Correlations, Polaron Size, and the Nature of the Self-Trapping Transition
• Polaron Mass and Electron-Phonon Correlations in the Holstein Model
• Holstein polaron in two and three dimensions by quantum Monte Carlo
• Franck-Condon Factors as Spectral Probes of Polaron Structure