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arXiv:2609.19450

Energy partitioning of wave packets in one-dimensional systems

Flávia B. Ramos, Imke Schneider, Sebastian Eggert, Rodrigo G. Pereira

Published Sep 16, 2026• 0 citations
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Abstract

We investigate the non-equilibrium dynamics of wave packets in a one-dimensional critical fermionic system and analyze the resulting partitioning of energy between emergent excitations. Starting from a Gaussian wave packet injected on top of the many-body ground state, we follow its real-time evolution using the time-dependent density-matrix renormalization group. We observe that interactions lead to fractionalization of the initial excitation into counter-propagating left- and right-moving modes, whose energies can be resolved in real space. To interpret these results, we employ Luttinger liquid theory, which allows us to derive analytical predictions for the energy carried by the emergent modes. We find good agreement between field-theoretical predictions and numerical simulations in the low-energy regime. In contrast to charge fractionalization, which is completely determined by the Luttinger liquid parameter, we show that energy partitioning is non-universal and depends on details of the injected wave packet, such as its width. Our results provide a real-space characterization of energy partitioning in one-dimensional systems and establish a quantitative comparison between non-equilibrium numerical simulations and the effective field-theory description.

DOI
10.48550/arxiv.2609.19450

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We investigate the non-equilibrium dynamics of wave packets in a one-dimensional critical fermionic system and analyze the resulting partitioning of energy between emergent excitations. Starting from a Gaussian wave packet injected on top of the many-body ground state, we follow its real-time evolution using the time-dependent density-matrix renormalization group. We observe that interactions lead to fractionalization of the initial excitation into counter-propagating left- and right-moving modes, whose energies can be resolved in real space. To interpret these results, we employ Luttinger liquid theory, which allows us to derive analytical predictions for the energy carried by the emergent modes. We find good agreement between field-theoretical predictions and numerical simulations in the low-energy regime. In contrast to charge fractionalization, which is completely determined by the Luttinger liquid parameter, we show that energy partitioning is non-universal and depends on details of the injected wave packet, such as its width. Our results provide a real-space characterization of energy partitioning in one-dimensional systems and establish a quantitative comparison between non-equilibrium numerical simulations and the effective field-theory description.
We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time evolution splits the signal into at least three distinct fractional charges moving with different velocities. A fractional left-moving charge is expected from conventional Luttinger liquid theory, but for the prediction of the two separate right-moving packets the nonlinearity of the dispersion must also be taken into account. This out-of-equilibrium protocol therefore allows a direct measurement of nonlinear interaction parameters, which also govern threshold singularities of dynamic response functions. The nonlinear Luttinger liquid theory also predicts the correct dynamics at low energies, where it agrees with the conventional Luttinger liquid. Moreover, at high energies, the wave packet dynamics reveals signatures of composite excitations containing two-particle bound states. Our results uncover a simple strategy to probe the nonlinear regime in time-resolved experiments in quantum wires and ultracold-atom platforms.
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Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires.
We compute the dynamics of localized excitations produced by a quantum quench in the spin-1/2 XXZ chain. Using numerics combining the density-matrix renormalization group and exact time evolution, as well as analytical arguments, we show that fractionalization due to interactions in the prequench state gives rise to ``ultrarelativistic'' density waves that travel at the maximum band velocity. The system is initially prepared in the ground state of the chain within the gapless XYXYXY phase, which admits a Luttinger liquid (LL) description at low energies and long wavelengths. The Hamiltonian is then suddenly quenched to a band insulator, after which the chain evolves unitarily. Through the gapped dispersion of the insulator spectrum, the postquench dynamics serve as a ``velocity microscope,'' revealing initial-state particle correlations via space-time density propagation. We show that the ultrarelativistic wave production is tied to the particular way in which fractionalization evades Pauli blocking in the zero-temperature initial LL state.