Characterizing the many-body localization transition by the dynamics of diagonal entropy

Based on the dynamics of diagonal entropy (DE), we provide a nonequilibrium method to study the properties of many-body localization (MBL) transition including the critical point and the universality class. By systematically studying the dynamical behaviors of DE in the fully explored Heisenberg spin chain with quasiperiodic field, we demonstrate the DE method can efficiently detect the transition point W-c between the thermal and MBL phase. We further use the method to study the MBL transition in the isotropic XX-ladder model, showing W-c similar to 8.05. We also widely explore the XX-ladder model with various parameters. Our results indicate that the MBL transition in the Heisenberg model and the XX-ladder model belong to distinct universality classes according to the obvious difference between the scaling exponents. These results can be tested in ongoing quantum simulation experiments with larger qubit numbers, since the diagonal elements of the density matrix directly yielding the DE can be easily obtained by repeatedly running single-shot measurements.