Entanglement Hamiltonian on subsystem at non-zero temperatures

The entanglement Hamiltonian is an effective Hamiltonian that describes the properties of a subsystem after taking the partial trace over the rest of the system. It plays a crucial role in various areas, including clustering of conditional mutual information, Hamiltonian learning, and quantum algorithms, etc. However, determining the structure of the entanglement Hamiltonian is generally a challenging problem. Even at sufficiently high temperatures, the standard cluster expansion method is indicated to be ineffective.

In this talk, I will present an alternative approach to studying the entanglement Hamiltonian that works across all temperature regimes. I will also discuss the limitations of this method and its implications for further research.