High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series
arXiv:1911.01345 · doi:10.1103/PhysRevB.101.045134
Abstract
We introduce a simple determinant diagrammatic Monte Carlo algorithm to compute the ground-state properties of a particle interacting with a Fermi sea through a zero-range interaction. The fermionic sign does not cause any fundamental problem when going to high diagram orders, and we reach order . The data reveal that the diagrammatic series diverges exponentially as with a radius of convergence . Furthermore, on the polaron side of the polaron-dimeron transition, the value of is determined by a special class of three-body diagrams, corresponding to repeated scattering of the impurity between two particles of the Fermi sea. A power-counting argument explains why finite is possible for zero-range interactions in three dimensions. Resumming the divergent series through a conformal mapping yields the polaron energy with record accuracy.
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