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Recent work on the subject of isolated quantum thermalization has suggestedthat an individual energy eigenstate of a non-integrable quantum system mayencode a significant amount of information about that system's Hamiltonian. Weprovide a theoretical argument, along with supporting numerics, that thisinformation includes the critical behaviour of a system with a second-order,finite-temperature phase transition.

Does a Single Eigenstate of a Hamiltonian Encode the Critical Behaviour of its Finite-Temperature Phase Transition?