Exact results for nonlinear Drude weights in the spin-1/2 XXZ chain

Abstract

Nonlinear Drude weight (NLDW) is a new concept which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-1/2 XXZ chain in the critical regime. The effects of the Dzyaloshinskii-Moriya interaction and an external magnetic field are also studied. Solving the Bethe equations numerically, we obtain these weights for very large system sizes and identify parameter regimes where the weights diverge in the thermodynamic limit. These divergences appear in all the orders studied in this paper and can be regarded as a universal feature of the NLDWs. We study the origin of these divergences and reveal that they result from $\text{nonanalytic}$ finite-size corrections to the ground state energy. Furthermore, we compute closed-form expressions for several weights in the thermodynamic limit and find excellent agreement with the numerical results.

arXiv comment6+15 pages, 2+2 figures

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• Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain
• Quantum turnstiles for robust measurement of full counting statistics
• Violation of the magnonic Wiedemann-Franz law in the strong nonlinear regime
• Energy-twisted boundary condition and response in one-dimensional quantum many-body systems
• Bloch oscillations in the spin-1/2 XXZ chain
• 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
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems