A Study On The Quench Dynamics Of The Haldane Model

Topology plays a vital role in contemporary condensed matter physics,in particular in the quantum Hall effect and topological insulators.Quantum entanglement provides an informative angle to understand the nontrivial topology in these systems.The robustness of the topology is also reflected in the dynamics of the topological systems.Quantum quench,among other dynamical driving methods,is a commonly used protocol in both theroetical and experimental studies.Motivated by the intricate connections among topology,quantum entanglement,and dynamics,we study the quench dynamics of the Haldane model via en-tanglement spectrum,as well as the probability density of selected entanglement eigenstates.In this paper we first study the quench dynamics of the Haldane model from a topological point of view via the entanglement spectrum and the probability density.Under a sudden quantum quench,the nontrivial topology of the pre-quench Hamiltonian is reflected in the zero-energy crossing(s)in the entanglement spectrum,when we partition the system into two strips,along which the translational invariance is preserved.The hallmark of topology survives,in the quench to a different topological phase,for a characteristic time that is determined both by the size of the bipartitioned system and the maximum velocity of the quasiparticles excited by quenching,even though the post-quench Hamiltonian belongs to a trivial phase.For the strip-shaped subsystem,the momentum dependence of the transverse velocity plays a crucial role in the out-of-equilibrium evolution of the entanglement properties.In the second part we explore the geometrical aspects of the post-quench evolution of the Haldane model.In the topological phase with Chern number C=1 the longitudinal mo-mentum of the zero-energy crossing in the entanglement spectrum varies as the time-reversal symmetry and inversion symmetry parameters are tuned.The characteristic momentum is a geometrical properties,at which the system can be mapped to a nontrivial one-dimensional model.We find that the momentum relaxes from the pre-quench value to post-quench one with oscillations that are dominated by energies associated with van Hove singularities.