Fractionalized wave packets from an artificial Tomonaga-Luttinger liquid

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 $P(t)=2 qDt$ 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 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 $P(t)=2 qDt$ 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.

arXiv:2610.22257Oct 15, 20260 citations

A classical Luttinger liquid

Riccardo Fantoni

arXiv:2402.13283Physica A Statistical Mechanics and its ApplicationsMay 23, 20250 citations

Debate over dispersion direction in a Tomonaga-Luttinger-liquid system

Hiroshi Nakatsuji, Kan Nakatsuji, F. Komori +1 more

Jan 1, 20120 citations

One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase

Marcello Dalmonte, Guido Pupillo, P. Zoller

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.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.

arXiv:1004.5035Physical Review LettersSep 28, 201071 citations

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)=2 qDt

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.