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

Jonas Vlietinck (UGent) , Kris Van Houcke (UGent) , Jan Ryckebusch (UGent)
Author
Organization
Project
FWO G.0119.12N and G.0115.12N
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.
Keywords
polaron systems, diagrammatic series, diagrammatic Monte Carlo, GROUND-STATE, ELECTRONS, FILMS

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## Citation

Chicago
Vlietinck, Jonas, Wim Casteels, Kris Van Houcke, Jacques Tempere, Jan Ryckebusch, and Josef T Devreese. 2015. “Diagrammatic Monte Carlo Study of the Acoustic and the Bose-Einstein Condensate Polaron.” New Journal of Physics 17.
APA
Vlietinck, J., Casteels, W., Van Houcke, K., Tempere, J., Ryckebusch, J., & Devreese, J. T. (2015). Diagrammatic Monte Carlo study of the acoustic and the Bose-Einstein condensate polaron. NEW JOURNAL OF PHYSICS, 17.
Vancouver
1.
Vlietinck J, Casteels W, Van Houcke K, Tempere J, Ryckebusch J, Devreese JT. Diagrammatic Monte Carlo study of the acoustic and the Bose-Einstein condensate polaron. NEW JOURNAL OF PHYSICS. 2015;17.
MLA
Vlietinck, Jonas, Wim Casteels, Kris Van Houcke, et al. “Diagrammatic Monte Carlo Study of the Acoustic and the Bose-Einstein Condensate Polaron.” NEW JOURNAL OF PHYSICS 17 (2015): n. pag. Print.
```@article{5895361,
abstract     = {We consider two large polaron systems that are described by a Fr{\"o}hlich 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{\textquoteright}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.},
articleno    = {033023},
author       = {Vlietinck, Jonas and Casteels, Wim and Van Houcke, Kris and Tempere, Jacques and Ryckebusch, Jan and Devreese, Josef T},
issn         = {1367-2630},
journal      = {NEW JOURNAL OF PHYSICS},
keyword      = {polaron systems,diagrammatic series,diagrammatic Monte Carlo,GROUND-STATE,ELECTRONS,FILMS},
language     = {eng},
pages        = {13},
title        = {Diagrammatic Monte Carlo study of the acoustic and the Bose-Einstein condensate polaron},
url          = {http://dx.doi.org/10.1088/1367-2630/17/3/033023},
volume       = {17},
year         = {2015},
}

```
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