Abstract
Motivated by recent experimental progress in the study of quantum systems far from equilibrium, we investigate the relation between several dynamical signatures of topology in the coherent time-evolution after a quantum quench. Specifically, we study the conditions for the appearance of entanglement spectrum crossings, dynamical quantum phase transitions, and dynamical Chern numbers. For non-interacting models, we show that in general there is no direct relation between these three quantities. Instead, we relate the presence of level crossings in the entanglement spectrum to localized boundary modes that may not be of topological origin in the conventional sense. Finally, we investigate how interactions influence the presence of entanglement spectrum crossings and dynamical quantum phase transitions, by means of time-dependent density matrix renormalization group simulations.
Highlights
Founded on the general notion of topological phases of matter [1,2,3], physical phenomena reflecting topological properties have been predicted and observed in a broad variety of systems
We have investigated the relations between entanglement spectrum crossings (ESCs), dynamical quantum phase transitions (DQPTs), and dynamical Chern number (DCN) in one-dimensional two-band models after quenches that were not necessarily restricted to a given AZ class
While the absence of a one-to-one correspondence between these indicators has been previously discussed in the context of symmetry-preserving quenches, here we showed that for general quenches their relation to topology is in some cases lost
Summary
Founded on the general notion of topological phases of matter [1,2,3], physical phenomena reflecting topological properties have been predicted and observed in a broad variety of systems. A common protocol to investigate the interplay between topology and dynamics is to perform a quantum quench, where the system is initialized in a topologically trivial state that can be prepared at low entropy, before some parameters in its Hamiltonian are changed to a topological regime In this scenario, numerous nonequilibrium signatures witnessing the change of topology have been identified [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49], including dynamical quantum phase transitions [36,37,38,39,40,41,42] (DQPTs), entanglement spectrum crossings [43,44,45] (ESCs), and a dynamical Chern number [46] (DCN).
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