Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids

We investigate wave packets generated by a local pulse electric field in a Tomonaga-Luttinger liquid (TLL) with a U(1) charge $q$. Bosonization shows that a local pulse field creates two counterpropagating packets with opposite accumulated charges $\pm qK$ and velocity $v$, where $K$ and $v$ are the TLL parameter and velocity. The packet motion produces a linearly growing charge polarization $P(t)=2qDt$ in the conducting TLL at non-equilibrium, allowing the Drude weight $D=vK$ to be extracted from real-time local dynamics. We test this local-packet description by time-dependent variational principle simulations of the spin-1/2 XXZ chain. The simulations visualize the density, current, energy, and entanglement profiles in the space-time plane and confirm the predicted packet charge and propagation velocity. We also show that excess energy and entanglement remaining near the pulse region are suppressed in the weak-pulse limit. Finally, the Drude weight obtained from the packet-induced polarization agrees with the exact Bethe-ansatz result, demonstrating local-packet spectroscopy of intrinsic transport in a TLL.