Distinguishing non-local orders, including global and topological orders of states through solely local operations and classical communications (LOCC), is a highly non-trivial and challenging task since the topology of states is determined by the global characteristics of the many-body system, such as the system's symmetry and the topological space it is based on. Here, we report that we reproduced the phase diagram of Ising model and symmetry protected topological phases using the quantum energy teleportation protocol, which foresees non-trivial energy transfer between remote observers using the entanglement nature of the ground state and LOCC. The model we use includes the Haldane model, the AKLT model, and the Kitaev model. Therefore, our method paves a new general experimental framework to determine and quantify phase transitions in various condensed matter physics and statistical mechanics.
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