We analyze the effective Hamiltonian for the 2T discrete time crystal (2T-DTC or DTC). This effective Hamiltonian is given by spin 1/2 many-body Hamiltonian which includes all-to-all coupling terms, thus being of infinite range. We describe the possible structure of the Hamiltonian, including many-body localized version which prevents thermalization. Finally, we show how the DTC melts when symmetry breaking terms are added.
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