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arXiv · 2502.05045

Energy dynamics in a class of local random matrix Hamiltonians

Klée Pollock·Jonathan D. Kroth·Nathan Pagliaroli·Thomas Iadecola·Jonathon Riddell
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Abstract

Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a conserved density, require a notion of spatially local interactions. We study the transport of the energy, the most basic conserved density, in few-body and 1D chains of nearest-neighbor random matrix terms that square to one. In the few-body but large local Hilbert space dimension case, we develop a mapping for the energy dynamics to a single-particle hopping picture. This allows for the computation of the energy density autocorrelators and an out-of-time-ordered correlator of the energy density. In the 1D chain, we numerically study the energy transport for a small local Hilbert space dimension. We also discuss the density of states throughout and touch upon the relation to free probability theory.

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Klée Pollock, Jonathan D. Kroth, Nathan Pagliaroli, Thomas Iadecola, Jonathon Riddell. 2025-02-07. Energy dynamics in a class of local random matrix Hamiltonians. https://doi.org/10.1103/5469-njfq

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