5 years ago

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

Mari Carmen Bañuls, arXiv:1801.05825, J. Ignacio Cirac, Tao Shi, Eugene Demler, Yuto Ashida

We provide a detailed formulation of the recently proposed variational approach [arXiv:1801.05825] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity systems. Motivated by the original ideas by 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 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. We use our approach to investigate the two-lead Kondo model and analyze its long-time spatiotemporal behavior and the influence of a magnetic field on the conductance. The obtained results are consistent with the previous findings in the Anderson model and the exact solutions at the Toulouse point.

Publisher URL: http://arxiv.org/abs/1802.03861

DOI: arXiv:1802.03861v1

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