Non-Hermitian quantum geometric tensor and nonlinear electrical response

Abstract

We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in non-Hermitian systems, generates an intrinsic nonlinear conductivity independent of the scattering time. In contrast, the full complex-valued QGT induces a distinct conductivity that depends explicitly on the wavepacket width. Using one- and two-dimensional non-Hermitian models, we establish a direct link between nonlinear dynamics and the QGT, thereby connecting quantum state geometry to observable transport phenomena. Crucially, we reveal that the finite wavepacket width fundamentally alters non-Hermitian transport -- a mechanism strictly absent in Hermitian systems. This framework elucidates non-Hermitian response theory by revealing how the complex geometry of quantum states, captured by the QGT, and the wavepacket width jointly encode transport in open and synthetic quantum matter.