Diagrammatic Monte Carlo study of the acoustic and the Bose–Einstein condensate polaron

Jonas Vlietinck,Kris Van Houcke,Jozef T Devreese,Jacques Tempere,Jan Ryckebusch,Wim Casteels

doi:10.1088/1367-2630/17/3/033023

Abstract

We consider two large polaron systems that are described by a Fröhlich type of Hamiltonian, namely the Bose–Einstein condensate (BEC) polaron in the continuum and the acoustic polaron in a solid. We present ground-state energies of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC) method and with a Feynman all-coupling approach. The DiagMC method evaluates up to very high order a diagrammatic series for the polaron’s self-energy. The Feynman all-coupling approach is a variational method that has been used for a wide range of polaronic problems. For the acoustic and BEC polaron both methods provide remarkably similar non-renormalized ground-state energies that are obtained after introducing a finite momentum cutoff. For the renormalized ground-state energies of the BEC polaron, there are relatively large discrepancies between the DiagMC and the Feynman predictions. These differences can be attributed to the renormalization procedure for the contact interaction.

Highlights

By virtue of the Coulomb interaction the presence of a charge carrier in a charged lattice induces a polarization
We show an example of the time dependence of the one-body self-energy Σ (τ, μ) for the Bose–Einstein condensate (BEC) polaron for qc = 200
We have studied the ground-state energies of the BEC polaron and the acoustic polaron, two large polaron systems that can be described by a Fröhlich type of Hamiltonian

Summary

Introduction

By virtue of the Coulomb interaction the presence of a charge carrier in a charged lattice induces a polarization. This effect is well-known from the description of an electron or a hole in a polar or ionic semiconductor. The term polaron was coined by Landau in 1933 [1] to denote the quasiparticle comprised of a charged particle coupled to a surrounding polarized lattice. For lattice-deformation sizes that are large compared to the lattice parameter, the lattice can be treated as a continuum. This system is known as a large polaron for which Fröhlich proposed the model Hamiltonian [4]

Methods

Results

Conclusion