Exact overlaps in the Kondo problem

Sergei L. Lukyanov (1) , Hubert Saleur (2, 3, 1) , Jesper L. Jacobsen (4, 5) , Romain Vasseur (6)

1 Department of Physics and Astronomy [Piscataway]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 UCLA - University of California [Los Angeles]
4 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
5 UPMC - Université Pierre et Marie Curie - Paris 6
6 LBNL - Lawrence Berkeley National Laboratory [Berkeley]

It is well known that the ground states of a Fermi liquid with and without a single Kondo impurity have an overlap which 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 nor 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.

Domains: High Energy Physics - Theory [hep-th]

Sergei L. Lukyanov, Hubert Saleur, Jesper L. Jacobsen, Romain Vasseur. Exact overlaps in the Kondo problem. Physical Review Letters, 2015, 114 (8), pp.080601. ⟨10.1103/PhysRevLett.114.080601⟩. ⟨cea-01229970⟩