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 – Published 11 July 2018

Abstract

We provide a detailed formulation of the recently proposed variational approach [Y. Ashida, T. Shi, M.-C. Bañuls, J. I. Cirac, and E. Demler, Phys. Rev. Lett. 121, 026805 (2018)] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity systems. Motivated by the original ideas of Tomonaga, Lee, Low, and Pines, we construct a canonical transformation that completely decouples the impurity from the bath degrees of freedom. By combining this transformation with a Gaussian ansatz for the fermionic bath, we obtain a family of variational many-body states that can efficiently encode the strong entanglement between the impurity and fermions of the bath. We give a detailed derivation of equations of motions in the imaginary- and real-time evolutions on the variational manifold. We benchmark our approach by applying it to investigate ground-state and dynamical properties of the anisotropic Kondo model and compare results with those obtained using the matrix-product state (MPS) ansatz. We show that our approach can achieve an accuracy comparable to MPS-based methods with several orders of magnitude fewer variational parameters than the corresponding MPS ansatz. Comparisons to the Yosida ansatz and the exact solution from the Bethe ansatz are also discussed. We use our approach to investigate the two-lead Kondo model and analyze its long-time spatiotemporal behavior and the conductance behavior at finite bias and magnetic fields. The obtained results are consistent with the previous findings in the Anderson model and the exact solutions at the Toulouse point.

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  • Received 19 February 2018

DOI:https://doi.org/10.1103/PhysRevB.98.024103

©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

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 (2018)

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Vol. 98, Iss. 2 — 1 July 2018

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