Explicit proof of Anderson's orthogonality catastrophe for the one-dimensional Fermi polaron with attractive interaction
Year: 2026
Type: article
Abstract: We provide a fully analytical derivation of Anderson's orthogonality catastrophe for the one dimensional Fermi polaron integrable model, describing a system of $N$ spin-up fermions, with fixed density $n=N/L$, interacting with a single spin-down fermion via an attractive contact potential. The proof combines the determinant representations of the norm of the many-body wave function and of its scalar product with the noninteracting ground state, obtained from the Bethe ansatz solution, with the special properties of Cauchy matrices. We derive the leading asymptotics of the two determinants in the thermodynamic limit and show that the quasi-particle residue $Z$ decays algebraically, $Z=W N^{-θ}$. We confirm that the Anderson exponent $θ$ is equal to $2δ_F^2/π^2$, where $δ_F$ is the Bethe-ansatz phase shift at the Fermi edge. We also derive the asymptotic behavior of the prefactor $W$ at strong coupling and compare it against exact numerics.
Source: Physical Review A
DOI: 10.1103/tgtd-3s4k
Author: Giuliano Orso
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203827742