Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

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.

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

“…We find the crossing point at ln(k F a) = −1.1 ± 0.2, which is in good agreement with previous studies 20 and experiment 12 and indistinguishable from the 2-ph result within our error bars, as could have been expected from the previous discussion.…”

“…Just as in Ref. 20 we will see that the ground-state energy remains close to the 1-ph result and that the 2-ph result is almost quantitatively exact, with the remaining fluctuations being very small in ph-order. The small parameter that can be exploited in the diagrammatic approach is the restricted phase space for the holes 7 .…”

“…One would hence expect that the success of diagMC for the Fermi-polaron can also be understood by identifying a (possibly emergent) small parameter. Recently, Vlietinck et al extended diagMC to the theoretical limit of pure 2D geometries 20 . For strong-enough interactions, they found growing fluctuations with expansion order that were claimed to be resummable and to result in a final answer close to the 1-ph result.…”

Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

“…are the same as found in [34,39]. In [36,42] the molecular regime, namely the region where the energy of the molecule under the effect of particle-hole fluctuations from the medium (dressed molecule) is lower than the polaron one, calculated with non-self-consistent methods happens from large and negative η up respectively to -0.97 or -0.95, above which the polaron energy will always be below the molecular energy. We define h = =-…”

“…The problem of one single impurity on top of a Fermi sea has been successfully solved with non-selfconsistent methods (see, e.g. [34,36,39,42,43]). However, we found the self-consistent one more suitable to handle in the investigation of the three-body problem of two impurities immersed in a Fermi sea, whose results are presented in the following sections.…”