Extracting Nonlinear Dynamical Response Functions from Time Evolution

Abstract

We develop a general framework based on the functional derivative to extract nonlinear dynamical response functions from the temporal evolution of physical quantities, without explicitly computing multipoint correlation functions. We validate our approach by calculating the second- and third-order optical responses in the Rice-Mele model and further apply it to a many-body interacting system using a tensor network method. This framework is broadly applicable to any method that can compute real-time dynamics, offering a powerful and versatile tool for investigating nonlinear responses in dynamical systems.

18 pages, 6 figures (including End Matter and Supplemental Material)

References in corpus (101)

• Real time evolution using the density matrix renormalization group
• The ITensor Software Library for Tensor Network Calculations
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Quantized circular photogalvanic effect in Weyl semimetals
• A real-space, rela-time method for the dielectric function
• Nonlinear Hall Effects
• Nonlinear optical signals and spectroscopy with quantum light
• Light-induced emergent phenomena in 2D materials and topological materials
• Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• Topology and geometry under the nonlinear electromagnetic spotlight
• Theory of Anderson pseudospin resonance with Higgs mode in superconductors
• Two-dimensional terahertz magnetic resonance spectroscopy of collective spin waves
• Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet
• Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
• Dynamics of the Kitaev-Heisenberg Model
• Spectral function of spinless fermions on a one-dimensional lattice
• Gauge covariances and nonlinear optical responses
• Nonlinear optics from an ab-initio approach by means of the dynamical Berry phase: Application to second- and third-harmonic generation in semiconductors
• Quantum geometry induced second harmonic generation
• Terahertz field-induced nonlinear coupling of two magnon modes in an antiferromagnet
• Resolving continua of fractional excitations by spinon echo in THz 2D coherent spectroscopy
• Nonlinear optical responses of crystalline systems: Results from a velocity gauge analysis
• Terahertz field-driven magnon upconversion in an antiferromagnet
• Infinite boundary conditions for matrix product state calculations
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Non-Equilibrium: Application to Pump-Probe Phenomena
• Theory of time-resolved optical spectroscopy on correlated electron systems
• Theory of two-dimensional nonlinear spectroscopy for the Kitaev spin liquid
• The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization
• High-harmonic generation in one-dimensional Mott insulator
• Systematic analysis method for nonlinear response tensors
• Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems
• Numerical method to compute optical conductivity based on pump-probe simulations
• Vibrational Coupling Modifies Spectral Diffusion in Core-Shell Colloidal Quantum Dots
• Basis-Independent Spectral Methods for Non-linear Optical Response in Arbitrary Tight-binding Models
• Nonlinear light-Higgs coupling in superconductors beyond BCS: Effects of the retarded phonon-mediated interaction
• Collective Modes in Excitonic Insulators: Effects of Electron-Phonon Coupling and Signatures in Optical Response
• Optical response of highly excited particles in a strongly correlated system
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic
• Higgs-mode resonance in third harmonic generation in NbN superconductors: multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence
• Non-linear Hall Effects: Mechanisms and Materials
• Linear and Nonlinear Optical Responses in Kitaev Spin Liquids
• Geometric aspects of nonlinear and nonequilibrium phenomena
• Revealing novel aspects of light-matter coupling in terahertz two-dimensional coherent spectroscopy: the case of the amplitude mode in superconductors
• Bulk Photovoltaic Effect Driven by Collective Excitations in a Correlated Insulator
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Extreme Terahertz Magnon Multiplication Induced by Resonant Magnetic Pulse Pairs
• Empowering Control of Antiferromagnets by THz-induced Spin Coherence
• Spectroscopic Signatures of Electron-Phonon Coupling in Silicon-Vacancy Centers in Diamond
• Decoding Ultrafast Polarization Responses in Lead Halide Perovskites by the Two-Dimensional Optical Kerr Effect
• Tailored subcycle nonlinearities of ultrastrong light-matter coupling
• Nonlinear polarization evolution using time-dependent density functional theory
• Photon echo from lensing of fractional excitations in Tomonaga-Luttinger spin liquid
• Extracting spinon self-energies from two-dimensional coherent spectroscopy
• Probing Inhomogeneous Cuprate Superconductivity by Terahertz Josephson Echo Spectroscopy
• Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
• Nonlinear spectroscopy of bound states in perturbed Ising spin chains
• Principles of 2D terahertz spectroscopy of collective excitations: the case of Josephson plasmons in layered superconductors
• Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy
• Higgs Oscillations in time-resolved Optical Conductivity
• Multidimensional Terahertz Probes of Quantum Materials
• Two-dimensional coherent spectrum of interacting spinons from matrix-product states
• Shedding Light on Microscopic Details: 2D Spectroscopy of 1D Quantum Ising Magnets
• Topological transition between competing orders in quantum spin chains
• Ultrafast transient interference in pump-probe spectroscopy of band and Mott insulators
• The spectral function of Mott-insulating Hubbard ladders: From fractionalized excitations to coherent quasi-particles
• Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy
• Two-dimensional coherent spectroscopy of trion-polaritons and exciton-polaritons in atomically thin transition metal dichalcogenides
• Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field
• Exploring Two-dimensional Coherent Spectroscopy with Exact Diagonalization: Spinons and Confinement in 1D Quantum Magnets
• Observation of Terahertz Spin Hall Conductivity Spectrum in GaAs with Optical Spin Injection
• Squeezed Josephson plasmons in driven YBa${}_2$Cu${}_3$O${}_{6+x}$
• Multidimensional Spectroscopy of Time-Dependent Impurities in Ultracold Fermions
• Process tensor approaches to modeling two-dimensional spectroscopy
• Photon echo and fractional excitation lensing of $S=1/2$ XY spin chain
• Effect of collective spin excitation on electronic transport in topological spin texture
• Direct and ultrafast probing of quantum many-body interaction and Mott-insulator transition through coherent two-dimensional spectroscopy
• A charge model as an effective model of one-dimensional Hubbard and extended Hubbard systems: its application to linear optical spectrum calculations in large systems based upon many-body Wannier functions
• Dynamics of fractionalized mean-field theories: consequences for Kitaev materials
• Second-order optical response of superconductors induced by supercurrent injection
• Spectral functions with infinite projected entangled-pair states
• Wannier-Stark ladders and Stark shifts of excitons in Mott insulators
• Anomalous suppression of photo-induced in-gap weight in the optical conductivity of a two-leg Hubbard ladder
• Generalized Linear Response Theory for Pumped Systems and its Application to Transient Optical Properties
• Revealing Quadrupolar Excitations with Non-Linear Spectroscopy
• Bulk photovoltaic effect in antiferromagnet: Role of collective spin dynamics
• Interedge spin resonance in the Kitaev quantum spin liquid
• Exploiting polarization dependence in two dimensional coherent spectroscopy: examples of Ce${}_2$Zr${}_2$O${}_7$ and Nd${}_2$Zr${}_2$O${}_7$
• Bound states and deconfined spinons in the dynamical structure factor of the $J_1-J_2$ spin-1 chain
• Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids
• Multidimensional coherent spectroscopy of correlated lattice systems
• Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy
• Signatures of spinon dynamics and phase structure of dipolar-octupolar quantum spin ices in two-dimensional coherent spectroscopy
• Keldysh crossover in one-dimensional Mott insulators
• Theory of symmetry-resolved quench-drive spectroscopy: Nonlinear response of phase-fluctuating superconductors
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Microscopic many-body theory of two-dimensional coherent spectroscopy of excitons and trions in atomically thin transition metal dichalcogenides
• Nonlinear Hall effect driven by spin-charge-coupled motive force
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects

Cited by in corpus (5)

• Unlocking Quantum Control and Multi-Order Correlations via Terahertz Two-Dimensional Coherent Spectroscopy
• A real-time approach to frequency-mixing spectroscopies: application to sum and difference frequency generation in two-dimensional crystals
• Temporal modulation of second harmonic generation in ferroelectrics by a pulsed electric field
• Tangent equations of motion for nonlinear response functions
• Two-dimensional THz spectroscopy in electronic systems: a many-body diagrammatic approach