Topological invariant in quench dynamics

Chao Yang; Shu Chen

doi:10.7498/aps.68.20191410

Journals >Acta Physica Sinica >Volume 68 >Issue 22 >Page 220304-1 > Article

Acta Physica Sinica
Vol. 68, Issue 22, 220304-1 (2019)

Topological invariant in quench dynamics

Chao Yang^1,* and Shu Chen^1,2,3,*

Author Affiliations

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

³Yangtze River Delta Physics Research Center, Liyang 213300, China

show less

DOI: 10.7498/aps.68.20191410 Cite this Article

Chao Yang, Shu Chen. Topological invariant in quench dynamics[J]. Acta Physica Sinica, 2019, 68(22): 220304-1 Copy Citation Text

show less

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

quench dynamics topological phase transition

$ h(k) = d_0(k){ I}+{ d}(k)\cdot{{\sigma}}, $

(1)

View in Article

$ \hat{\rho}_{\pm}(k) = |\psi_{\pm}(k)\rangle\langle\psi_{\pm}(k)| = \frac{1}{2}[1\pm\hat{{ d}}(k)\cdot{ \sigma}], $

(2)

View in Article

$ \rho(k,t) = {\rm e}^{-{\rm i} h^{\rm f}(k)t}\rho(k,0){\rm e}^{{\rm i} h^{\rm f}(k)t}. $

(3)

View in Article

$ \rho(k,t) = \frac{1}{2}[1-\hat{{ d}}(k,t)\cdot{ \sigma}], $

(4)

View in Article

\begin{aligned} \hat{d} (k, t) = & {\hat{d}}^{i} \cos (2 | d^{f} | t) + 2 {\hat{d}}^{f} ({\hat{d}}^{i} \cdot {\hat{d}}^{f}) \\ \times \sin^{2} (| d^{f} | t) + {\hat{d}}^{i} \times {\hat{d}}^{f} \sin (2 | d^{f} | t), \end{aligned}

(5)

View in Article

$ C_{\rm dyn}^{m} = \frac{1}{4{\text{π}} }\int_{k_m}^{k_{m+1}}{\rm d} k\int_{0}^{\textstyle\frac{{\text{π}} }{|{ d}^{\rm f}|}}{\rm d}t^{\prime} (\hat{{ d}}\times\partial_{t^{\prime}} \hat{{ d}})\cdot\partial_k, \hat{{ d}} ,$

(6)