我们提出了一般条件的相位带交叉的一类周期性驱动的可积系统表示的自由费米子模型进行任意周期性的驱动协议的频率$ω_D$。这些模型为$d=1$中的Ising和$XY$模型、$d=2$中的Kitaev模型、几种超导体以及石墨烯和拓扑绝缘体表面上的狄拉克费米子提供了表示。我们的研究结果表明，在系统哈密顿（这是遍历在一个有限的速率在动态）的临界点/区域的存在下，可能会改变的条件发生在临界模式的相位带交叉。我们还表明，对于$d>1$，相位带交叉留下他们的印记，这些模型的等时间的非对角费米子相关函数;这种相关函数，$F_{\vec k_0}( ω_0)$的傅立叶变换，有最大值和最小值在特定的频率可以直接相关的$ω_D$和相位带交叉的时间在$\vec k = \vec k_0$。我们讨论了我们的结果的意义的背景下，通用的哈密顿与$N>2$相带和驱动哈密顿的基本对称性。
英文摘要：
We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $ω_D$. These models provide a representation for the Ising and $XY$ models in $d=1$, the Kitaev model in $d=2$, several kinds of superconductors, and Dirac fermions in graphene and atop topological insulator surfaces. Our results demonstrate that the presence of a critical point/region in the system Hamiltonian (which is traversed at a finite rate during the dynamics) may change the conditions for phase band crossings that occur at the critical modes. We also show that for $d>1$, phase band crossings leave their imprint on the equal-time off-diagonal fermionic correlation functions of these models; the Fourier transforms of such correlation functions, $F_{\vec k_0}( ω_0)$, have maxima and minima at specific frequencies which can be directly related to $ω_D$ and the time at which the phase bands cross at $\vec k = \vec k_0$. We discuss the significance of our results in the contexts of generic Hamiltonians with $N>2$ phase bands and the underlying symmetry of the driven Hamiltonian.
The University of Burdwan（布尔达万大学）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Poornaprajna Institute of Scientific Research（普尔纳普拉尼亚科学研究学院）
