Parametric instability in periodically driven Luttinger liquids

Abstract

We analyze the properties of a Luttinger liquid under the influence of a periodic driving of the interaction strength. Irrespective of the details the driven system develops an instability due to a parametric resonance. For slow and fast driving, however, we identify intermediate long-lived meta-stable states at constant time-averaged internal energies. Due to the instability perturbations in the fermionic density are amplified exponentially leading to the buildup of a superlattice. The momentum distribution develops a terrace structure due to scattering processes that can be associated with the absorption of quanta of the driving frequency.

7 pages, 4 figures

References in corpus (37)

• Many-Body Physics with Ultracold Gases
• Nonequilibrium dynamics of closed interacting quantum systems
• Kondo Physics in a Single Electron Transistor
• A Tunable Kondo Effect in Quantum Dots
• The Kondo Effect in the Unitary Limit
• The Luttinger model following a sudden interaction switch-on
• Superfluid-insulator transition in a periodically driven optical lattice
• Bosonization for Beginners --- Refermionization for Experts
• Nonequilibrium dynamical mean-field theory
• Universal theory of nonlinear Luttinger liquids
• Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations
• Universality of the Kondo Effect in a Quantum Dot out of Equilibrium
• Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
• Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators
• Dielectric breakdown of Mott insulators in dynamical mean-field theory
• Dynamical band flipping in fermionic lattice systems: An ac-field-driven change of the interaction from repulsive to attractive
• Nonequilibrium Steady State of Photoexcited Correlated Electrons in the Presence of Dissipation
• Suppression of Kondo effect in a quantum dot by external irradiation
• Quenching Bloch oscillations in a strongly correlated material
• The Anderson Model out of equilibrium: Time dependent perturbations
• Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions
• Damping of Bloch oscillations in the Hubbard model
• Kondo effect in AC transport through Quantum dots
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
• Non-equilibrium dynamics of the driven Hubbard model
• Dimensional Crossover Driven by an Electric Field
• Nonlinear Response of a Kondo system: Direct and Alternating Tunneling Currents
• Slow quench dynamics of periodically driven quantum gases
• Non-linear response of a Kondo system: Perturbation approach to the time dependent Anderson impurity model
• Nonlinear current response of an isolated system of interacting fermions
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
• Integrable Mott insulators driven by finite electric field
• Photo-induced Tomonaga-Luttinger-like liquid in a Mott insulator
• Non-equilibrium steady state in a periodically driven Kondo model
• Parametric resonance and spin-charge separation in 1D fermionic systems
• Interference of parametrically driven one-dimensional ultracold gases

Cited by in corpus (21)

• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
• Prethermal Floquet Steady States and Instabilities in the Periodically Driven, Weakly Interacting Bose-Hubbard Model
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Mechanism of Ultrafast Relaxation of a Photo-Carrier in Antiferromagnetic Spin Background
• Aperiodically driven integrable systems and their emergent steady states
• Parametric Instability Rates in Periodically-Driven Band Systems
• Observation of Massless and Massive Collective Excitations with Faraday Patterns in a Two-Component Superfluid
• Fibonacci steady states in a driven integrable quantum system
• Floquet resonant states and validity of the Floquet-Magnus expansion in the periodically driven Friedrichs models
• Non-equilibrium Floquet steady states of time-periodic driven Luttinger liquids
• The Floquet Fermi Liquid
• Time evolution during and after finite-time quantum quenches in Luttinger liquids
• Exact results in Floquet coin toss for driven integrable models
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Marginal quenches and drives in Tomonaga-Luttinger liquids
• Chiral Luttinger liquids in graphene tuned by irradiation
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• Chiral Instabilities in Driven-Dissipative Quantum Liquids
• Energy current and energy fluctuations in driven quantum wires