Energy dynamics in a class of local random matrix Hamiltonians

• URL: http://arxiv.org/abs/2502.05045v3
• Date: Tue, 12 Aug 2025 16:53:53 GMT
• Title: Energy dynamics in a class of local random matrix Hamiltonians
• Authors: Klée Pollock, Jonathan D. Kroth, Nathan Pagliaroli, Thomas Iadecola, Jonathon Riddell,
• Abstract summary: We study the transport of the energy in few-body and 1D chains of nearest-neighbor random matrix terms that square to one.<n>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.<n>In the 1D chain, we numerically study the energy transport for a small local Hilbert space dimension.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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