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

Abstract

We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace.

Transport of Neutral Optical Excitations Using Electric Fields

“…A similar expression ∼ G e (k)G e (k + Ω) occurs in the definition of π(p; Ω) in Eq. (44) and contains information about the electron mobility. The latter expression can be simplified by expanding the Green's functions in terms of delta functions around the quasiparticle resonance = ξ k .…”

Spectra of heavy polarons and molecules coupled to a Fermi sea

“…The variational energy has recently been verified using diagrammatic quantum Monte Carlo [16][17][18][19][20][21]. The situation is quite different for the impurity spectrum, which is the actual quantity measured in experiments: in Monte Carlo, extracting the spectrum is difficult due to the infamous analytical continuation problem, and only few definite statements can be made [22].…”

Ab initioLattice Results for Fermi Polarons in Two Dimensions

“…But with increasing particle interaction strength, molecules will form by capturing one or even two particles from the Fermi sea, and this behavior has been shown to depend on the mass ratio of the two components of the Fermi gas for the 3D case [2][3][4][5][6][7][8][9][10]. In 1D, the exact analytical solution for equal masses shows that the polaron-molecule transition is a smooth crossover [11,12].In 2D the Fermi polaron properties have been studied using different theoretical and experimental approaches, and these have predicted various scenarios for the existence or absence of a polaron-molecule transition [13][14][15][16][17][18][19][20][21]. The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21].…”

“…The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21]. The diag MC method uses a worm algorithm to stochastically sample Feynman diagrams to high orders in the coupling constant.…”