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

Article

关键词: MATRIX PRODUCT STATES;    MANY-BODY SYSTEM;    RENORMALIZATION-GROUP;    ANDERSON MODEL;    PHASE-TRANSITIONS;    LOW-TEMPERATURES;    COHERENT STATES;    FERMION SYSTEMS;    MAGNETIC-FIELD;    DOTS;   

DOI  :  10.1103/PhysRevB.98.024103

来源: SCIE

【 摘 要 】

We provide a detailed formulation of the recently proposed variational approach [Y. Ashida, T. Shi, M.-C. Banuls, 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.

【 授权许可】

Free