Nonlinear Drude weight (NLDW) is a generalization of the linear Drude weight, which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-$\frac{1}{2}$ 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 Letter and can be regarded as a generic feature of the NLDWs. We study the origin of these divergences and reveal that they result from 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.

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• Electrical properties
• Transport phenomena
• 1-dimensional systems
• Lattice models in condensed matter
• Many-body techniques
• Numerical techniques