Exact overlaps in the Kondo problem

TL;DR

This paper derives an exact formula for the overlap between ground states of Kondo systems with different couplings, revealing universal behavior beyond perturbative methods and Bethe ansatz.

Contribution

It introduces a novel exact formula for ground state overlaps in the Kondo problem using integrable quantum field theory techniques.

Findings

Overlap is finite in the thermodynamic limit for different Kondo couplings.

Overlap depends universally on the ratio of Kondo temperatures.

The formula matches density matrix renormalization group calculations.

Abstract

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.