Hierarchical hydrodynamics in long-range multipole-conserving systems

Abstract

This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical sequence of multipole-conserving models characterized by power-law decaying couplings. Although the moments are always globally conserved, adjusting the power-law exponents of the couplings induces various regimes in which only a subset of multipole moments are effectively locally conserved. We examine the late-time hydrodynamics analytically and numerically using an effective classical framework, uncovering a rich dynamical phase diagram that includes subdiffusion, conventional diffusion, and Lévy flights. Our results are unified in an analytic reciprocal relationship that captures the nested hierarchy of hydrodynamics in multipole conserving systems where only a subset of the moments are locally conserved. Moreover, we extend our findings to higher dimensions and explore the emergence of long-time scales, reminiscent of pre-thermal regimes, in systems with low charge density. Lastly, we corroborate our results through state-of-the-art numerical simulations of a fully quantum long-range dipole-conserving system and discuss their relevance to trapped-ion experimental setups.

16+3 pages, 9 figures

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• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• The Kernel Polynomial Method
• Lévy walks
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Cited by in corpus (10)

• Many-Body Non-Hermitian Skin Effect for Multipoles
• Generating Lattice Non-invertible Symmetries
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Emergent Fracton Hydrodynamics of Ultracold Atoms in Partially Filled Landau Levels
• Bosonic Quantum Breakdown Hubbard Model
• Topological Dipole Insulator
• Entanglement dynamics from universal low-lying modes
• Domain coarsening in fractonic systems: a cascade of critical exponents
• Hierarchy of degenerate stationary states in a boundary-driven dipole-conserving spin chain
• Expediting quantum state transfer through the long-range extended XY model