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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.
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Submitted on : Tuesday, November 17, 2015 - 3:13:53 PM
Last modification on : Monday, December 13, 2021 - 9:16:04 AM

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



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