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Article Dans Une Revue Physical Review B Année : 2020

High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series

Felix Werner
Riccardo Rossi

Résumé

We introduce a simple determinant diagrammatic Monte Carlo algorithm to compute the ground-stateproperties of a particle interacting with a Fermi sea through a zero-range interaction. The fermionic sign doesnot cause any fundamental problem when going to high diagram orders, and we reach order N = 30. The datareveal that the diagrammatic series diverges exponentially as (−1/R) N with a radius of convergence R < 1.Furthermore, on the polaron side of the polaron-dimeron transition, the value of R is determined by a specialclass of three-body diagrams, corresponding to repeated scattering of the impurity between two particles ofthe Fermi sea. A power-counting argument explains why finite R is possible for zero-range interactions in threedimensions. Resumming the divergent series through a conformal mapping yields the polaron energy with recordaccuracy.
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Dates et versions

hal-02868438 , version 1 (20-01-2022)

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Kris van Houcke, Felix Werner, Riccardo Rossi. High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series. Physical Review B, 2020, 101 (4), pp.045134. ⟨10.1103/PhysRevB.101.045134⟩. ⟨hal-02868438⟩
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