Linear response as a singular limit for a periodically driven closed quantum system

Abstract

We address the issue of the validity of linear response theory for a closed quantum system subject to a periodic external driving. Linear response theory (LRT) predicts energy absorption at frequencies of the external driving where the imaginary part of the appropriate response function is different from zero. Here we show that, for a fairly general non-linear many-body system on a lattice subject to an extensive perturbation, this approximation should be expected to be valid only up to a time $t^{\ast }$ depending on the strength of the driving, beyond which the true coherent Schrödinger evolution departs from the linear response prediction and the system stops absorbing energy form the driving. We exemplify this phenomenon in detail with the example of a quantum Ising chain subject to a time-periodic modulation of the transverse field, by comparing an exact Floquet analysis with the standard results of LRT. In this context, we also show that if the perturbation is just local, the system is expected in the thermodynamic limit to keep absorbing energy, and LRT works at all times. We finally argue more generally the validity of the scenario presented for closed quantum many-body lattice systems with a bound on the energy-per-site spectrum, discussing the experimental relevance of our findings in the context of cold atoms in optical lattices and ultra-fast spectroscopy experiments.

31 pages, 7 figures. Improved final discussion, added appendix on the Bogoliubov-de Gennes-Floquet approach

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Real time evolution using the density matrix renormalization group
• Dynamical control of matter-wave tunneling in periodic potentials
• Observation of photon-assisted tunneling in optical lattices
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point

Cited by in corpus (24)

• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Onset of Floquet Thermalisation
• The quantum Ising chain for beginners
• Dynamical Freezing and Scar Points in Strongly Driven Floquet Matter: Resonance vs Emergent Conservation Laws
• Loschmidt echo and dynamical fidelity in periodically driven quantum systems
• From localization to anomalous diffusion in the dynamics of coupled kicked rotors
• Homogeneous Floquet time crystal protected by gauge invariance
• Dynamic steady-state of periodically-driven quantum systems
• Spin and topological order in a periodically driven spin chain
• Asymptotic work statistics of periodically driven Ising chains
• Quantum Critical Scaling under Periodic Driving
• Entanglement entropy in a periodically driven Ising chain
• Non equilibrium phase transitions and Floquet Kibble-Zurek scaling
• Entanglement entropy in a periodically driven quantum Ising chain
• Quantum quenches, linear response and superfluidity out of equilibrium
• Quenching and generation of random states in a kicked Ising model
• A study of excess energy and decoherence factor of a qubit coupled to a one dimensional periodically driven spin chain
• Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
• Unscrambling of single-particle wave functions in systems localized through disorder and monitoring
• Dynamical phase transition in the 1D-transverse field Ising chain characterized by the transverse magnetization spectral function
• Resilience of hidden order to symmetry-preserving disorder
• Energy and particle currents in a driven integrable system
• Scrambling in Ising spin systems with periodic transverse magnetic fields
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains