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
±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.
We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|(β), with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a "Luttinger staircase." Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.