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Exact overlaps in the Kondo problem.

Sergei L Lukyanov1, Hubert Saleur1,2,3, Jesper L Jacobsen4,5

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|March 14, 2015
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Summary
This summary is machine-generated.

The Anderson orthogonality catastrophe describes decaying ground state overlap in Fermi liquids. We found a finite overlap between ground states with different Kondo couplings, providing an exact formula for this quantum impurity phenomenon.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Quantum Field Theory

Background:

  • The ground states of Fermi liquids with and without a single Kondo impurity exhibit an overlap that decays with system size, known as the Anderson orthogonality catastrophe.
  • This phenomenon is crucial for understanding quantum quenches in impurity systems.

Purpose of the Study:

  • To investigate the overlap between ground states with different Kondo coupling strengths.
  • To derive an exact formula for this overlap, which is a universal function of Kondo temperatures.
  • To overcome limitations of traditional methods like perturbation theory and the Bethe ansatz.

Main Methods:

  • Utilized the integrable structure of the corresponding quantum field theory.
  • Developed an exact analytical formula for the ground state overlap.
  • Validated the formula using extensive Density Matrix Renormalization Group (DMRG) calculations.

Main Results:

  • Demonstrated that ground states with distinct Kondo couplings possess a finite overlap in the thermodynamic limit.
  • Established that this overlap is a universal function dependent on the ratio of Kondo temperatures.
  • Provided an exact formula for this overlap, confirmed by numerical simulations.

Conclusions:

  • The study presents a novel exact solution for a key quantity in quantum impurity systems.
  • The findings offer new insights into quantum quenches and the behavior of strongly correlated electron systems.
  • The developed formula provides a powerful tool for future research in condensed matter theory.