A Numerical Renormalization Group approach to Non-Equilibrium Green's Functions for Quantum Impurity Models

Abstract

We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfills the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion $U>0$ is switched on at $t=0$, and the asymptotic steady-state spectral functions are obtained for various values of $U$ as well as magnetic field strength $H$ and temperature $T$. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite $U$. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nano-devices.

21 pages, 6 figures

References in corpus (7)

• The numerical renormalization group method for quantum impurity systems
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
• New method for studying steady states in quantum impurity problems: The interacting resonant level model

Cited by in corpus (2)

• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems