Quantum adiabatic polarons by translationally invariant perturbation theory

TL;DR

This paper applies a translationally invariant quantum perturbation theory to analyze polarons in a 1D lattice, calculating higher-order corrections and exploring the adiabatic crossover, providing a comprehensive quantum description of polaron properties.

Contribution

It introduces a fourth-order perturbation calculation within a translationally invariant framework, extending understanding of polaron energy, width, and mass across different regimes.

Findings

Fourth-order self-energy diagrams calculated exactly.

Polaron energy and properties match traditional broken symmetry results.

Identifies the adiabatic crossover while the polaron width is large.

Abstract

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency omega0, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/omega0>1 for g/omega0~(t/omega0)^{1/4} when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/omega0)^{1/2}>g/omega0>(t/omega0)^{1/4}>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset.