title: Exact overlaps in the Kondo problem.
abstract: It is well known that the ground states of a Fermi liquid with and without a single Kondo impurity have an overlap that decays as a power law of the system size, expressing the Anderson orthogonality catastrophe. Ground states with two different values of the Kondo couplings have, however, a finite overlap in the thermodynamic limit. This overlap, which plays an important role in quantum quenches for impurity systems, is a universal function of the ratio of the corresponding Kondo temperatures, which is not accessible using perturbation theory or the Bethe ansatz. Using a strategy based on the integrable structure of the corresponding quantum field theory, we propose an exact formula for this overlap, which we check against extensive density matrix renormalization group calculations.
authors.affiliation: Physics Department, Rutgers University, Piscataway, New Jersey 08854, USA.
authors.forename: Sergei L
authors.initials: SL
authors.lastname: Lukyanov
authors.affiliation: Physics Department, Rutgers University, Piscataway, New Jersey 08854, USA.|Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.|Institut de Physique Théorique, CEA Saclay, 91191 Gif Sur Yvette, France.
authors.forename: Hubert
authors.initials: H
authors.lastname: Saleur
authors.affiliation: LPTENS, École Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.|Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France.
authors.forename: Jesper L
authors.initials: JL
authors.lastname: Jacobsen
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA.|Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA.
authors.forename: Romain
authors.initials: R
authors.lastname: Vasseur