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arXiv:2410.10571 · Physical Review Research

Propagation of two-particle correlations across the chaotic phase for interacting bosons

Óscar Dueñas, David Peña, Alberto Rodríguez

Published Feb 10, 2025• 3 citations
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Abstract

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.

DOI
10.1103/physrevresearch.7.l012031

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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.
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.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.
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Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatio-temporal chaotic properties have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusions, respectively. Our results also provide new insights into the dynamics of interacting quantum systems in the semiclassical limit.
Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatio-temporal chaotic properties have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusions, respectively. Our results also provide new insights into the dynamics of interacting quantum systems in the semiclassical limit.