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

TL;DR

This paper develops a unified framework linking emergent hydrodynamics and low energy spectra of Lindblad operators to understand charge transport in complex many-body systems with various symmetries and interactions.

Contribution

It introduces a mapping between averaged dynamics and Lindblad spectra, enabling analysis of diffusive and anomalous relaxation in systems with conserved multipole moments.

Findings

Explicit construction of dispersive excited states using a single mode approximation

Identification of exotic Krylov-space hydrodynamics with diffusive relaxation despite dipole conservation

Numerical verification of diffusive behavior in systems with 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.