Operator-level characterization of the interacting entanglement Hamiltonian

Develop a genuine operator-level characterization of the entanglement Hamiltonian in interacting integrable models, thereby clarifying the microscopic origin of entanglement dynamics and connecting the thermodynamic cumulant description with the operator-based quasiparticle formulation available in free systems.

Background

The paper derives a relation between the cumulants of the entanglement Hamiltonian after a quantum quench and the cumulants of suitably defined conserved currents in integrable systems. This analysis is thermodynamic and provides direct access to cumulants, but it does not yield an explicit operator representation of the entanglement Hamiltonian in interacting models.

In free systems, an operator-level description can be constructed using coarse-grained quasiparticle number operators, and this formulation makes the transport interpretation transparent. The authors identify obtaining an analogous operator-level formulation for interacting models as an important unresolved problem, which could explain the microscopic origin of the observed entanglement dynamics and establish a bridge between the interacting thermodynamic framework and the free-system quasiparticle picture.