In the 1D attractive Fermi polaron the quasi-particle residue decays as Z = W N^{-2 δ_F² / π²} with δ_F the Bethe-ansatz phase shift at the Fermi edge and W obtained numerically.
Gaudin, Un systeme a une dimension de fermions en interaction, Physics Letters A24, 55 (1967)
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Explicit proof of Anderson's orthogonality catastrophe for the one-dimensional Fermi polaron with attractive interaction
In the 1D attractive Fermi polaron the quasi-particle residue decays as Z = W N^{-2 δ_F² / π²} with δ_F the Bethe-ansatz phase shift at the Fermi edge and W obtained numerically.