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

Jonas Vlietinck (1) , Wim Casteels (2, 3) , Kris Van Houcke (4, 1) , Jacques Tempere (3, 5) , Jan Ryckebusch (1) , Jozef T Devreese (3)

1 Department of Physics and Astronomy [Ghent]
2 MPQ (UMR_7162) - Laboratoire Matériaux et Phénomènes Quantiques
3 TQC - Theory of Quantum systems and Complex systems
4 LPS - Laboratoire de Physique Statistique de l'ENS
5 Lyman Laboratory of Physics

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.

Mots clés: polaron systems; diagrammatic Monte Carlo; diagrammatic series

Domaines: Physique [physics]

Jonas Vlietinck, Wim Casteels, Kris Van Houcke, Jacques Tempere, Jan Ryckebusch, et al.. Diagrammatic Monte Carlo study of the acoustic and the Bose–Einstein condensate polaron. New Journal of Physics, 2015, 17 (3), pp.033023. ⟨10.1088/1367-2630/17/3/033023⟩. ⟨hal-01250087⟩