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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.
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Keywords:
- topological phase transition/
- quench dynamics
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AZ class TRS PHS CS $(s, t, d, d_{//}, \text{original~class,} P)$ $K_{\rm C}^{\rm U/A}(K_{\rm R}^{\rm U/A})$ Dynamical realization Stable against dispersion A 0 0 0 $(\sim, \sim, 2, \sim, A, \sim)$ ${\mathbb Z}$ 0 0 AIII 0 0 1 $(0, 1, 2, 1, A, \bar{U})$ ${\mathbb Z}\bigoplus{\mathbb Z}$ ${\mathbb Z}$ 0 AI 1 0 0 $(\sim, \sim, 2, \sim, AI, \sim)$ 0 0 0 BDI 1 1 1 $(0, 3, 2, 1, AI, \bar{A}_{+}^{+})$ ${\mathbb Z}$ ${\mathbb Z}$ ${\mathbb Z}_2$ D 0 1 0 $(2, \sim, 2, 1, A, \bar{A}^{+})$ ${\mathbb Z}_2$ ${\mathbb Z}_2$ ${\mathbb Z}_2$ DIII –1 1 1 $(4, 1, 2, 1, AII, \bar{A}_{+}^{+})$ ${\mathbb Z}_2\bigoplus{\mathbb Z}_2$ ${\mathbb Z}_2$ 0 AII –1 0 0 $(\sim, \sim, 2, \sim, AII, \sim)$ ${\mathbb Z}_2$ 0 0 CII –1 –1 1 $(4, 3, 2, 1, AII, \bar{A}_{+}^{-})$ ${\mathbb Z}$ ${\mathbb Z}$ 0 C 0 –1 0 $(6, \sim, 2, 1, A, \bar{A}^{-})$ 0 0 0 CI 1 –1 1 $(0, 1, 2, \sim, AI, \bar{A}_{+}^{-})$ 0 0 0 
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