  Distinguishing non-local orders, including global and topological orders of
states through solely local measurements 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 (SPT) 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.
