Temperature-dependent energy diffusion in chaotic spin chains

We study the temperature dependence of energy diffusion in two chaotic gapped quantum spin chains, a tilted-field Ising model and an XZ model, using open-system approach. introduce imbalance by coupling chain to thermal baths at its boundary nonequilibrium steady states resulting Lindblad dynamics matrix product operator ansatz for density matrix. define effective local profile comparing reduced matrices state with those uniform state. then measure current variety driving temperatures extract constant. For we are able well below gap find regime dilute excitations where rare three-body collisions control diffusion. A kinetic correctly predicts observed exponential increase constant low temperatures. only access intermediate high relative gap, show that data described expansion around infinite limit. also discuss limitations particular scheme suggest lower can be accessed larger baths.