Second-order functional renormalization group approach to quantum wires out of equilibrium
arXiv:2004.03946 · doi:10.1103/PhysRevB.102.235113
Abstract
The functional renormalization group (FRG) provides a flexible tool to study correlations in low-dimensional electronic systems. In this paper, we present a novel FRG approach to the steady-state of quantum wires out of thermal equilibrium. Our method is correct up to second order in the two-particle interaction and accounts for inelastic scattering. We combine semi-analytic solutions of the flow equations with MPI parallelization techniques, which allows us to treat systems of up to 60 lattice sites. The equilibrium limit is well-understood and serves as a benchmark. We compute effective distribution functions, the local density of states, and the steady-state current and demonstrate that all of these quantities depend strongly on the choice of the cutoff employed within the FRG. Non-equilibrium is plagued by the lack of physical arguments in favor of a certain cutoff as well as by the appearance of secular higher-order terms which are only partly included in our approach. This demonstrates the inadequacy of a straightforward second-order FRG scheme to study interacting quantum wires out of equilibrium in the absence of a natural cutoff choice.
References in corpus (44)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Functional renormalization group approach to correlated fermion systems
- On Many-Body Localization for Quantum Spin Chains
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Equilibrium states of generic quantum systems subject to periodic driving
- The approach to thermal equilibrium in quantized chaotic systems
- Long-time behavior of periodically driven isolated interacting lattice systems
- Many-body localization in periodically driven systems
- Integrals of motion in the Many-Body localized phase
- One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
- Prethermalization
- Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
- Finite-temperature transport in one-dimensional quantum lattice models
- Real-time path integral approach to nonequilibrium many-body quantum system
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
- Universal theory of nonlinear Luttinger liquids
- Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
- Quantum quench dynamics
- Periodic thermodynamics of isolated systems
- Nonequilibrium electron transport using the density matrix renormalization group
- Review: Local Integrals of Motion in Many-Body Localized systems
- Iterative real-time path integral approach to nonequilibrium quantum transport
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
- Real-Time Diagrammatic Monte Carlo for Nonequilibrium Quantum Transport
- Numerically exact path integral simulation of nonequilibrium quantum transport and dissipation
- Nonequilibrium functional renormalization group for interacting quantum systems
- Nonequilibrium functional RG with frequency dependent vertex function: A study of the single impurity Anderson model
- Functional renormalization group for non-equilibrium quantum many-body problems
- A finite-frequency functional RG approach to the single impurity Anderson model
- Time Dependent Floquet Theory and Absence of an Adiabatic Limit
- Applying Adaptive Time-Dependent DMRG to Calculate the Conductance of Strongly Correlated Nanostructures
- A renormalization group approach to time dependent transport through correlated quantum dots
- Functional renormalization group study of the interacting resonant level model in and out of equilibrium
- Properties of multi-particle Green and vertex functions within Keldysh formalism
- Flow Equation Calculation of Transient and Steady State Currents in the Anderson Impurity Model
- Functional Renormalization Group Approach for Inhomogeneous Interacting Fermi-Systems
- Detecting phases in one-dimensional many-fermion systems with the functional renormalization group
- Interacting fermions in one dimension: The Tomonaga-Luttinger model
- Keldysh Functional Renormalization Group Treatment of Finite-Ranged Interactions in Quantum Point Contacts
- The Functional Renormalization Group for Zero-Dimensional Quantum Systems in and out of Equilibrium
- Second order functional renormalization group approach to one-dimensional systems in real and momentum space
Cited by in corpus (3)
- Review of recent developments of the functional renormalization group for systems out of equilibrium
- Finite-bias transport through the interacting resonant level model coupled to a phonon mode -- a functional renormalization group study
- Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity