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Abstract

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.

Keywords:

topological phase transition/
quench dynamics

Authors and contacts

Yang Chao¹,
Chen Shu^1,2,3

Corresponding author:Yang Chao,yangchao@iphy.ac.cn; Chen Shu,schen@iphy.ac.cn

Funds:Project supported by the State Key Development Program for Basic Research of China (Grant No. 2016YFA0300600) and the National Natural Science Foundation of China (Grant Nos. 11425419, 11974413)

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Cited By

DownLoad: Full-Size Img PowerPoint

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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Vol. 68, Issue 22 - 2019-11-20

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