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Emergent symmetry is one of the characteristic phenomena in deconfinedquantum critical point (DQCP). As its nonequilibrium generalization, the dualdynamic scaling was recently discovered in the nonequilibrium imaginary-timerelaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we studythe nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model,which also hosts a DQCP belonging to the same equilibrium universality class.We not only verify the universality of the dual dynamic scaling at the criticalpoint, but also investigate the breakdown and the vestige of the dual dynamicscaling when the tuning parameter is away from the critical point. We alsodiscuss its possible experimental realizations in devices of quantum computers.

Dual dynamic scaling in deconfined quantum criticality