Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
arXiv:2304.13028 · doi:10.1103/PhysRevLett.131.220403
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.
arXiv comment7 + 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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