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

Nonlinear Drude weight (NLDW) is a generalization of the linear Drude weight [1], 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 at zero temperature [2,3]. The analysis of the NLDWs based on the Bethe ansatz reveals that they exhibit convergence, power-law, and logarithmic divergence with system size, depending on the anisotropy parameter Δ. The divergence occurs in all orders and can be regarded as a generic feature of the NLDWs. We study the origin of the divergences and find that they result from nonanalytic finite-size corrections to the ground state energy. Furthermore, for the convergent cases, we compute closed-form expressions for several weights in the thermodynamic limit by using the Wiener-Hopf method.

[1] H. Watanabe and M. Oshikawa, Phys. Rev. B 102, 165137 (2020)

[2] Y. Tanikawa, K. Takasan, and H. Katsura, Phys. Rev. B 103, L201120 (2021)

[3] Y. Tanikawa and H. Katsura, arXiv:2107.13784 (2021)