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Energy dynamics in a class of local random matrix Hamiltonians

Klée Pollock1,*, Jonathan D. Kroth1, Nathan Pagliaroli2,†, Thomas Iadecola1,3, and Jonathon Riddell4,‡

  • *Contact author: kleep@iastate.edu
  • †Contact author: npagliar@uwo.ca
  • ‡Contact author: j.p.riddell@bham.ac.uk
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Phys. Rev. Research 7, 033129 – Published 6 August, 2025

DOI: https://doi.org/10.1103/5469-njfq

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, which we dub the “Haar-Ising” local random matrix model. 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. Throughout, we discuss the density of states and touch upon the relation to free probability theory.

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Phys. Rev. Research 7, 033129– Published 6 August, 2025
  • Received 9 April 2025
  • Accepted 21 July 2025
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