Energy dynamics in a class of local random matrix Hamiltonians

TL;DR

This paper investigates energy transport in local random matrix Hamiltonians, revealing how energy dynamics behave in few-body and 1D chain systems, with analytical and numerical insights into autocorrelators and density of states.

Contribution

It introduces a mapping of energy dynamics to a single-particle hopping model for large local Hilbert spaces and explores energy transport in 1D chains with numerical methods.

Findings

Energy autocorrelators computed analytically in few-body systems.

Numerical results on energy transport in 1D chains.

Discussion of density of states and relation to free probability.

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.