Analysis of the nonlinear Drude weights in the one-dimensional Hubbard model

The Drude weight represents the component of the electrical conductivity corresponding to the DC response and serves as a key quantity that distinguishes metals from insulators. Recently, nonlinear Drude weights (NLDWs) have been introduced as extensions of the linear Drude weight, providing a means to characterize nonlinear transport phenomena [1]. Although NDWs have been well investigated in spin systems and free-electron systems, their behavior in strongly correlated electron systems remains largely unexplored.

In this work, we study the NLDWs in the one-dimensional Hubbard model, a prototypical example of a strongly correlated electron system. Using the Bethe ansatz, we compute the NLDWs and analyze their finite-size corrections in both the insulating and metallic phases. Furthermore, we reveal the hyperscaling relations of NLDWs near the metal-insulator transition point.

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