Type-I Dynamical Quantum Phase Transitions in Topological Quantum Many-body Systems

Recent advances in quantum technologies underscore the importance of understanding nonequilibriumdynamics in quantum many-body systems, with dynamical quantum phasetransitions (DQPTs) serving as crucial probes. This proposal focuses on type-I DQPTs, whichare revealed through the long-time average of observables following sudden parameterquenches. While type-I DQPTs have been theorized and observed in spin and bosonicsystems, their study in topological systems, characterized by global invariants, remainsunderexplored. Our project aims to bridge this gap by investigating type-I DQPTs in atopological insulator with next-nearest-neighbor hoppings, which exhibits a rich phasediagram encompassing various topological phases. We will develop a suitable orderparameter using a modified reduced density matrix approach and employ advancedsimulation techniques such as exact diagonalization and density matrix renormalization groupto study the system's post-quench dynamics. By analyzing the scaling behavior of the orderparameter across different quench paths, we will characterize type-I dynamical phaseboundaries and contrast them with the equilibrium phase diagram. This research will enhanceour understanding of the interplay between topology and non-local hoppings in nonequilibriumquantum dynamics, paving the way for advancements in quantum technologies.