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 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.

4.5+7 pages. 3 figures

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Cited by in corpus (7)

• Universal spatial correlations in the anisotropic Kondo screening cloud: analytical insights and numerically exact results from a coherent state expansion
• Universal Single-Frequency Oscillations in a Quantum Impurity System After a Local Quench
• Towards a Non-equilibrium Bethe ansatz for the Kondo Model
• Universal Entanglement Dynamics following a Local Quench
• Fidelities in the spin-boson model
• Many-body dynamics of the decay of excitons of different charges in a quantum dot
• Ground state overlap knows about ultraviolet dynamics: results for the Kondo model