Information as a hydrodynamic slow mode: operator spreading in the Memory Matrix Formalism

McCulloch, Ewan R. ORCID: 0000-0003-4521-7628 (2022). Information as a hydrodynamic slow mode: operator spreading in the Memory Matrix Formalism. University of Birmingham. Ph.D.

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Abstract

The study of many-body quantum systems is an incredibly diverse and active field of research, connecting many disparate fields, from condensed matter systems to quantum gravity and black hole physics. Understanding the far-from-equilibrium physics of these systems is of particular importance as state-of-the-art experimental platforms now allow for exceptional control over many-body dynamics. A focal point in the study of far-fromequilibrium many-body physics is the quantum foundation of statistical mechanics, and in quantum chaos and thermalisation in particular. In this thesis we investigate a concept closely related to thermalisation, known as scrambling, which explains the apparent loss of the initial state data as the ‘hiding’ of information in increasingly non-local and difficult to measure observables. In systems with local interactions, information (and operators) spreads ballistically, at a speed set by the butterfly velocity. We show that a standard hydrodynamical tool, the memory matrix formalism (MMF), can be repurposed to investigate the transport of quantum information, making explicit the connection between operator spreading and hydrodynamics. By viewing information as hydrodynamical slow mode in the MMF, the ballistic spreading of information is natural on symmetry grounds. This new perspective also serves as a starting point for the perturbative calculation of information transport. Much of what is known about operator spreading is restricted to minimally structured models, where almost all of the spatio-temporal structure (such as spatial and time translation symmetries) has been relinquished. In this thesis, we apply the MMF to different one-dimensional circuit models with large local Hilbert space (dimension q), each with different spatio-temporal symmetries, and compute information transport coefficients perturbatively in the small parameter 1/q. We find that both spatial and time translation symmetries lead to an enhancement of information transport.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):