Renormalization group for open quantum systems using environment temperature as flow parameter
arXiv:2111.07320 · doi:10.21468/SciPostPhys.12.4.121
Abstract
We present the -flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature of its environment. This has the key advantage that it can be formulated directly in real time, making it particularly suitable for transient dynamics, while automatically accumulating the full temperature dependence of transport quantities. We solve the -flow equations numerically for the example of the single impurity Anderson model. We benchmark in the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger using results obtained by the functional renormalization group, density-matrix renormalization group and the quantum Monte Carlo method. Here we find quantitative agreement even in the worst case of strong interactions and low temperatures, indicating the reliability of the method. For transient charge currents we find good agreement with results obtained by the 2PI Green's function approach. Furthermore, we analytically show that the short-time dynamics of both local and non-local observables follow a universal temperature-independent behaviour when the metallic reservoirs have a flat wide band.
24 pages, 5 figures; resubmission to SciPost Physics; Fig. 2b contained curves which were insufficiently converged. This has been corrected without affecting any part of the text and conclusions
References in corpus (19)
- Real time evolution using the density matrix renormalization group
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
- Transforming quantum operations: quantum supermaps
- 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
- Iterative real-time path integral approach to nonequilibrium quantum transport
- Kinetic Equations for Transport Through Single-Molecule Transistors
- A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
- Transient dynamics of the Anderson impurity model out of equilibrium
- Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
- Fermionic superoperators for zero-temperature non-linear transport: real-time perturbation theory and renormalization group for Anderson quantum dots
- Real-time renormalization group in frequency space: A 2-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field
- Real-time renormalization group and cutoff scales in nonequilibrium applied to an arbitrary quantum dot in the Coulomb blockade regime
- Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings
- Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling
- Charge fluctuations in nonlinear heat transport
- Feynman-Vernon influence functional approach to quantum transport in interacting nanojunctions: An analytical hierarchical study
- The connection between time-local and time-nonlocal perturbation expansions