淬火动力学中的拓扑不变量

Topological invariant in quench dynamics

本文主要介绍了近期关于一维拓扑能带系统中淬火动力学的研究.从两能带模型入手介绍了动力学陈数,并给出它与初末态拓扑不变量之间的关系.进而通过将一维含时波函数看作为1+1维母哈密顿量的基态,给出了Altland-Zirnbauer分类对应的动力学拓扑分类,并简要介绍了动力学的体边对应以及空间无序和能带色散对纠缠谱交叉的影响.最后还介绍了利用超导量子比特模拟观测到动力学陈数.

In this review,we give a brief review on the recent progress in the theoretical research of quench dynamics in topological band systems.Beginning with two band models,we introduce conception of dynamical Chern number and give the connection between the dynamical Chern number and topological invariant in the corresponding equilibrium systems.Then by studying the 1+1 dimensional parent Hamiltonian,we show the complete dynamical classification of Altland-Zirnbauer classes,and show the crossing of entanglement spectrum as a feature of dynamical bulk edge correspondence.Furthermore,we consider the impact of the disorder and band dispersion.At last,we show the experimental simulation of dynamical Chern number by a superconducting qubit system.