Low temperature acoustic polaron localization

TL;DR

This paper investigates the phase transition of an acoustic polaron from localized to unlocalized states at low temperatures using path integral Monte Carlo simulations, revealing a discontinuous change in potential energy.

Contribution

It provides numerical evidence of a phase transition in the acoustic polaron model, characterizing the transition as a discontinuity in potential energy related to coupling strength.

Findings

Discontinuous potential energy at the phase transition

Localized electron state at strong coupling

Extended electron state at weak coupling

Abstract

We calculate the low temperature properties of an acoustic polaron in three dimensions in thermal equilibrium at a given temperature using a specialized path integral Monte Carlo method. In particular we find numerical evidence that the chosen Hamiltonian for the acoustic polaron describes a phase transition from a localized state to an unlocalized state for the electron as the phonons-electron coupling constant decreases. The phase transition manifests itself with a jump discontinuity in the potential energy as a function of the coupling constant. In the weak coupling regime the electron is in an extended state whereas in the strong coupling regime it is found in a self-trapped state.