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Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

Jonas Vlietinck (UGent) , Jan Ryckebusch (UGent) and Kris Van Houcke (UGent)
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Abstract
We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron Z factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.
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GASES

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Chicago
Vlietinck, Jonas, Jan Ryckebusch, and Kris Van Houcke. 2014. “Diagrammatic Monte Carlo Study of the Fermi Polaron in Two Dimensions.” Physical Review B 89 (8).
APA
Vlietinck, J., Ryckebusch, J., & Van Houcke, K. (2014). Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions. PHYSICAL REVIEW B, 89(8).
Vancouver
1.
Vlietinck J, Ryckebusch J, Van Houcke K. Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions. PHYSICAL REVIEW B. 2014;89(8).
MLA
Vlietinck, Jonas, Jan Ryckebusch, and Kris Van Houcke. “Diagrammatic Monte Carlo Study of the Fermi Polaron in Two Dimensions.” PHYSICAL REVIEW B 89.8 (2014): n. pag. Print.
@article{4298474,
  abstract     = {We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron Z factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.},
  articleno    = {085119},
  author       = {Vlietinck, Jonas and Ryckebusch, Jan and Van Houcke, Kris},
  issn         = {1098-0121},
  journal      = {PHYSICAL REVIEW B},
  keyword      = {GASES},
  language     = {eng},
  number       = {8},
  pages        = {6},
  title        = {Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions},
  url          = {http://dx.doi.org/10.1103/PhysRevB.89.085119},
  volume       = {89},
  year         = {2014},
}

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