Effective dissipation rate in a Liouvillian graph picture of high-temperature quantum hydrodynamics

Abstract

At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that the emergence of this dissipative long-wavelength dynamics from the system's unitary microscopic dynamics is controlled by the structure of the \textit{Liouvillean graph} of the system's Hamiltonian, that is, the graph induced on Pauli strings by commutation with that Hamiltonian. The Liouvillean graph decomposes naturally into subgraphs of Pauli strings of constant diameter, and the coherent dynamics of these subgraphs determines the rate at which operator weight spreads to long operators. This argument provides a quantitative theory of the emergence of a dissipative effective dynamics from unitary microscopic dynamics; it also leads to an effective model with Hilbert space dimension linear in system size and exponential in the UV cutoff for diffusion.

Updated with changes in light of referee response, incl. discussion of chaos in pools of long operators. Close to published version

References in corpus (9)

• The Kernel Polynomial Method
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Quantum dynamics of thermalizing systems
• Renormalization-group study of the many-body localization transition in one dimension
• Stability of superdiffusion in nearly integrable spin chains
• Many-body localization near the critical point
• Operator backflow and the classical simulation of quantum transport
• Time-evolution of local information: thermalization dynamics of local observables
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Cited by in corpus (7)

• Quantum dynamics in one and two dimensions via recursion method
• The operator growth hypothesis in open quantum systems
• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
• Quantum many-body simulations with PauliStrings.jl
• Pseudomode expansion of many-body correlation functions
• Emergent random matrix universality in quantum operator dynamics
• Robustness of near-thermal dynamics on digital quantum computers