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arXiv:2603.04373 · New Journal of Physics

Dynamical Behaviour of Density Correlations Across the Chaotic Phase for Interacting Bosons

Óscar Dueñas, Alberto Rodríguez

quant-phcond-mat.quant-gasSubmitted Mar 4, 2026• Announced Mar 5, 2026• 0 citations
v1 · Mar 4, 2026v2 · Apr 22, 2026
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Abstract

We investigate the propagation of two-point density correlations in the one-dimensional Bose-Hubbard Hamiltonian in the thermodynamic limit in terms of the correlation transport distance (CTD), an experimentally measurable magnitude that characterizes the spatial spreading of correlations in time. We confirm that the integrable limits of the model exhibit CTD ballistic growth, while the onset of the chaotic phase leads to the emergence of a pronounced sub-ballistic regime, in agreement with previous results for finite systems. By a meticulous analysis of the spatio-temporal correlation profiles, we show that the correlation front nonetheless propagates ballistically for all interaction strengths, and that the chaos-induced slowdown of the CTD originates from the emergence of long-time distance-dependent correlation tails, together with an enhanced decay of the correlation front amplitude. Our results thus provide a detailed characterization of correlation transport that goes beyond a simple light-cone picture.

Journal reference
New J. Phys. 28, 054506 (2026)
DOI
10.1088/1367-2630/ae6475
Comments
15 pages, 8 figures

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We investigate the propagation of two-point density correlations in the one-dimensional Bose-Hubbard Hamiltonian in the thermodynamic limit in terms of the correlation transport distance (CTD), an experimentally measurable magnitude that characterizes the spatial spreading of correlations in time. We confirm that the integrable limits of the model exhibit CTD ballistic growth, while the onset of the chaotic phase leads to the emergence of a pronounced sub-ballistic regime, in agreement with previous results for finite systems. By a meticulous analysis of the spatio-temporal correlation profiles, we show that the correlation front nonetheless propagates ballistically for all interaction strengths, and that the chaos-induced slowdown of the CTD originates from the emergence of long-time distance-dependent correlation tails, together with an enhanced decay of the correlation front amplitude. Our results thus provide a detailed characterization of correlation transport that goes beyond a simple light-cone picture.
We analyze the propagation of experimentally relevant two-particle correlations for one-dimensional interacting bosons, and give evidence that many-body chaos induces the emergence of an effective diffusive regime for the fully coherent correlation dynamics, characterized by an interaction dependent diffusion coefficient, which we estimate. This result supports very recent experimental observations, and paves the way toward an efficient description of the dynamical behavior of nonintegrable complex many-body systems. Furthermore, we show that the dynamical features within experimentally accessible time scales of a conveniently defined two-particle correlation transport distance provide a direct and unambiguous characterization of many-body quantum chaos in perfect agreement with its spectral identification.
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We analyze the quench dynamics of a one-dimensional bosonic Mott insulator and focus on the time evolution of density correlations. For these we identify a pronounced propagation front, the velocity of which, once correctly extrapolated at large distances, can serve as a quantitative characteristic of the many-body Hamiltonian. In particular, the velocity allows the weakly interacting regime, which is qualitatively well described by free bosons, to be distinguished from the strongly interacting one, in which pairs of distinct quasiparticles dominate the dynamics. In order to describe the latter case analytically, we introduce a general approximation to solve the Bose-Hubbard Hamiltonian based on the Jordan-Wigner fermionization of auxiliary particles. This approach can also be used to determine the ground-state properties. As a complement to the fermionization approach, we derive explicitly the time-dependent many-body state in the noninteracting limit and compare our results to numerical simulations in the whole range of interactions of the Bose-Hubbard model.
Lieb-Robinson and related bounds set an upper limit on the speed at which information propagates in nonrelativistic quantum systems. Experimentally, light-cone-like spreading has been observed for correlations in the Bose-Hubbard model (BHM) after a quantum quench. Using a two-particle irreducible (2PI) strong-coupling approach to out-of-equilibrium dynamics in the BHM we calculate both the group and phase velocities for the spreading of single-particle correlations in one, two, and three dimensions as a function of interaction strength. Our results are in quantitative agreement with measurements of the speed of spreading of single-particle correlations in both the one- and two-dimensional BHM realized with ultracold atoms. They also are consistent with the claim that the phase velocity rather than the group velocity was observed in recent experiments in two dimensions. We demonstrate that there can be large differences between the phase and group velocities for the spreading of correlations and explore how the anisotropy in the velocity varies across the phase diagram of the BHM. Our results establish the 2PI strong-coupling approach as a powerful tool to study out-of-equilibrium dynamics in the BHM in dimensions greater than one.
We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization approach and the Bose-Hubbard model using the time-dependent density-matrix renormalization group method. For short distances, correlations follow a power law with distance with an exponent given by the adiabatic approximation. In contrast, for long distances, correlations decay algebraically with an exponent understood within the sudden quench approximation. This long distance regime is separated from an intermediate distance one by a generalized Lieb-Robinson criterion. At long times, in this intermediate regime, bosonization predicts that single-particle correlations decay following a stretched exponential, an unconventional behavior. We develop here an intuitive understanding for the propagation of correlations, in terms of a generalized light cone, applicable to a large variety of systems and quench forms.
We analyze the propagation of correlations after a sudden interaction change in a strongly interacting quantum system in contact with an environment. In particular, we consider an interaction quench in the Bose-Hubbard model, deep within the Mott-insulating phase, under the effect of dephasing. We observe that dissipation effectively speeds up the propagation of single-particle correlations while reducing their coherence. In contrast, for two-point density correlations, the initial ballistic propagation regime gives way to diffusion at intermediate times. Numerical simulations, based on a time-dependent matrix product state algorithm, are supplemented by a quantitatively accurate fermionic quasiparticle approach providing an intuitive description of the initial dynamics in terms of holon and doublon excitations.