Quantum Quench and $f$-Sum Rules on Linear and Non-linear Conductivities

Abstract

Considering a quench process in which an electric field pulse is applied to the system, "$f$-sum rule" for the conductivity for general quantum many-particle systems is derived. It is furthermore extended to an infinite series of sum rules, applicable to the nonlinear conductivity at every order.

arXiv comment5 pages, 1 figure; v3: numerical factors corrected

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• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
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• Exact results for nonlinear Drude weights in the spin-1/2 XXZ chain
• Quantum entanglement and quantum geometry measured with inelastic X-ray scattering
• Divergent nonlinear response from quasiparticle interactions
• Spectral Density and Sum Rules for Second-Order Response Functions
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
• Using Disorder to Identify Bogoliubov Fermi-Surface States
• Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain
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• Quantum turnstiles for robust measurement of full counting statistics
• Violation of the magnonic Wiedemann-Franz law in the strong nonlinear regime
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Bloch oscillations in the spin-1/2 XXZ chain
• Energy-twisted boundary condition and response in one-dimensional quantum many-body systems
• Non-linear Transport by Bethe Bound States
• Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations
• Drude weights in one-dimensional systems with a single defect
• Hydrodynamic non-linear response of interacting integrable systems
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• The Bloch theorem in the presence of an additional conserved charge
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective