Transport interpretation of entanglement Hamiltonian cumulants in integrable quantum quenches

Abstract: We study the dynamics of the cumulants of the entanglement Hamiltonian in interacting integrable models following global quantum quenches. Building on recent results based on space-time duality, we show that these cumulants are exactly given by the cumulants of currents of suitable conserved charges evaluated in the macrostate selected by the initial state. This establishes a direct connection between entanglement dynamics and transport, providing a transport counterpart to the quasiparticle picture that successfully describes the evolution of the von Neumann entropy. In the free-fermion and conformal limits, our results reduce to the difference between the current cumulants carried by right- and left-moving excitations, recovering previously known expressions. In interacting integrable models, where a decomposition into independent right and left movers is no longer meaningful at the operator level, a similar structure survives at the level of the entanglement spectrum, yielding a unified description of entanglement Hamiltonian fluctuations across free, conformal, and interacting integrable systems.