| Summary: | The study of topologically ordered states has given rise to a growing interest in symmetry-protected states in quantum matter. Recently, this theory has been extended to quantum many-body systems, which demonstrate ordered states at low temperatures. An example of this is the discrete time crystal (DTC), which has been demonstrated in a real quantum computer and in driven systems. These states are periodic in time and are protected from disorder to a certain extent. In general, DTCs can be classified into two phases: the stable many-body localization (MBL) state and the disordered thermal state. This work demonstrates the by generalizing DTCs to two dimensions, where there was an decrease in the thermal noise and an increase in the operating range of the MBL range in the presence of disorder.
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