Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

Yuto Ashida, Tao Shi, Mari Carmen Bañuls, J. Ignacio Cirac, and Eugene Demler
Phys. Rev. Lett. 121, 026805 – Published 11 July 2018

Abstract

A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical transformation that completely decouples the impurity and bath degrees of freedom. Combining it with Gaussian states, we present a family of many-body states to efficiently encode nontrivial impurity-bath correlations. We demonstrate its successful application to the anisotropic and two-lead Kondo models by studying their spatiotemporal dynamics and universal behavior in the correlations, relaxation times, and the differential conductance. We compare them to previous analytical and numerical results. In particular, we apply our method to study new types of nonequilibrium phenomena that have not been studied by other methods, such as long-time crossover in the ferromagnetic easy-plane Kondo model. The present approach will be applicable to a variety of unsolved problems in solid-state and ultracold-atomic systems.

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  • Received 19 February 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.026805

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuto Ashida1,*, Tao Shi2,3,†, Mari Carmen Bañuls3, J. Ignacio Cirac3, and Eugene Demler4

  • 1Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 2CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
  • 3Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
  • 4Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

  • *ashida@cat.phys.s.u-tokyo.ac.jp
  • tshi@itp.ac.cn

See Also

Variational principle for quantum impurity systems in and out of equilibrium: Application to Kondo problems

Yuto Ashida, Tao Shi, Mari Carmen Bañuls, J. Ignacio Cirac, and Eugene Demler
Phys. Rev. B 98, 024103 (2018)

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Vol. 121, Iss. 2 — 13 July 2018

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