Driven by rapid advancements in quantum simulation capabilities across diverse physical platforms, open quantum systems are now of great interest, with special focus on thermalization processes of interacting many-body systems. Various techniques have been used to study operator spreading, to characterize entanglement dynamics, and even to identify exotic phases enabled by dynamical symmetries.
This talk will present a novel perspective on dynamical quantum systems that is capable of reproducing many previous results under a single intuitive framework and enables new results in symmetry-constrained systems. This is accomplished via a mapping between the dynamics averaged over Brownian random time evolution and the low-energy spectrum of a Lindblad superoperator, which acts as an effective Hamiltonian in a doubled Hilbert space. Doing so, we identify emergent hydrodynamics governing charge transport in open quantum systems with various symmetries, constraints, and ranges of interactions. 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 diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Therefore, we provide a simple, general, and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution, and by extension, thermalizing quantum systems.
O. Ogunnaike, J. Feldmeier, J.Y. Lee, "Unifying Emergent Hydrodynamics and Lindbladian Low-Energy Spectra across Symmetries, Constraints, and Long-Range Interactions," arXiv:2304.13028 (accepted to PRL)
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