Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions

Abstract

We identify emergent hydrodynamics governing charge transport in Brownian random circuits with various symmetries, constraints, and ranges of interactions. This is accomplished via a mapping between the averaged dynamics and the low energy spectrum of a Lindblad operator, which acts as an effective Hamiltonian in a doubled Hilbert space. By explicitly constructing dispersive excited states of this effective Hamiltonian using a single mode approximation, we provide a comprehensive understanding of diffusive, subdiffusive, and superdiffusive relaxation in many-body systems with conserved multipole moments and variable interaction ranges. Our approach further allows us to identify exotic Krylov-space-resolved hydrodynamics exhibiting diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Our approach provides a general and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution.

7 + 8 pages, 4 figures; We previously omitted a Note Added section in the PRL version by mistake. This update corrects that oversight to properly reflect the intended content

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Cited by in corpus (33)

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• Hydrodynamics as the effective field theory of strong-to-weak spontaneous symmetry breaking
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• An exactly solvable dissipative spin liquid
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
• Spontaneous breaking of U(1) symmetry at zero temperature in one dimension
• A Bound on Thermalization from Diffusive Fluctuations
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Quadratic dispersion relations in gapless frustration-free systems
• Spin Liquid and Superconductivity emerging from Steady States and Measurements
• Emergent Fracton Hydrodynamics of Ultracold Atoms in Partially Filled Landau Levels
• Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results
• Subdiffusive transport in the Fredkin dynamical universality class
• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Bosonic Quantum Breakdown Hubbard Model
• Rigorous lower bound on dynamical exponents in gapless frustration-free systems
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Effective Conformal Field Theory generated from Pure and Dephased Chern insulator
• Mixed-state learnability transitions in monitored noisy quantum dynamics
• Frustration-free free fermions and beyond
• Frustration-free free fermions
• Dynamics in the presence of local symmetry-breaking impurities
• Non-Universality from Conserved Superoperators in Unitary Circuits
• Entanglement dynamics from universal low-lying modes
• Quasi-local Frustration-Free Free Fermions
• Emergent Viscous Hydrodynamics From a Single Quantum Particle
• Domain coarsening in fractonic systems: a cascade of critical exponents
• Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor