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Emergent topology under slow nonadiabatic quantum dynamics
Physical Review A ( IF 2.6 ) Pub Date : 
Junchen Ye, Fuxiang Li

Characterization of equilibrium topological quantum phases by non-equilibrium quench dynamics provides a novel and efficient scheme in detecting topological invariants defined in equilibrium. Nevertheless, most of the previous studies have focused on the ideal sudden quench regime. Here we provide a generic non-adiabatic protocol of slowly quenching the system Hamiltonian, and investigate the non-adiabatic dynamical characterization scheme of topological phase. The {} quench protocol is realized { by introducing a Landau-Zener problem with inverse proportional time-dependence}, and it can describe, in a unified way, the crossover from sudden quench regime (deep non-adiabatic limit) to adiabatic regime. By analytically obtaining the final state vector after non-adiabatic evolution, we can calculate the time-averaged spin polarization and the corresponding topological spin texture. We find that the topological invariants of the post-quench Hamiltonian are characterized directly by the values of spin texture on the band inversion surface. Compared to the sudden quench regime, where one has to take an additional step to calculate the {} of spin polarization, this non-adiabatic characterization provides a {} scheme in detecting the topological invariants. { By studying the slow quench dynamics of 3D topological phases, we show that our findings are not restricted to 1D and 2D topological phases under inverse proportional time-dependent quench protocol, but are also valid for higher dimensional systems or different quench protocols.

中文翻译:

慢非绝热量子动力学下的新兴拓扑

通过非平衡猝灭动力学表征平衡拓扑量子相,为检测平衡中定义的拓扑不变量提供了一种新颖而有效的方案。尽管如此,以前的大多数研究都集中在理想的猝灭状态。在这里,我们提供了一种缓慢淬灭系统哈密顿量的通用非绝热协议,并研究了拓扑相的非绝热动力学表征方案。{}通过引入具有反比例时间依赖性的Landau-Zener问题来实现{}猝灭协议,它可以统一描述从突然猝灭状态(深非绝热极限)到绝热状态的过渡。通过解析获得非绝热演化后的最终状态向量,我们可以计算时间平均自旋极化和相应的拓扑自旋纹理。我们发现,淬火后哈密顿量的拓扑不变量直接由带反转表面上的自旋织构值表征。与必须采取额外步骤来计算自旋极化{}的突然猝灭状态相比,这种非绝热特性为检测拓扑不变量提供了{}方案。{通过研究3D拓扑相的缓慢淬灭动力学,我们发现我们的发现不限于与时间成反比的逆向淬灭协议下的1D和2D拓扑相,而且对于高维系统或不同的淬灭协议也有效。我们发现,淬火后哈密顿量的拓扑不变量直接由带反转表面上的自旋织构值表征。与必须采取额外步骤来计算自旋极化{}的突然猝灭状态相比,这种非绝热特性为检测拓扑不变量提供了{}方案。{通过研究3D拓扑相的缓慢淬灭动力学,我们发现我们的发现不限于与时间成反比的逆向淬灭协议下的1D和2D拓扑相,而且对于高维系统或不同的淬灭协议也有效。我们发现,淬火后哈密顿量的拓扑不变量直接由带反转表面上的自旋织构值表征。与必须采取额外步骤来计算自旋极化{}的突然猝灭状态相比,这种非绝热特性为检测拓扑不变量提供了{}方案。{通过研究3D拓扑相的缓慢淬灭动力学,我们发现我们的发现不限于与时间成反比的逆向淬灭协议下的1D和2D拓扑相,而且对于高维系统或不同的淬灭协议也有效。在必须采取额外步骤来计算自旋极化{}的情况下,这种非绝热特性为检测拓扑不变量提供了{}方案。{通过研究3D拓扑相的缓慢淬灭动力学,我们发现我们的发现不限于与时间成反比的逆向淬灭协议下的1D和2D拓扑相,而且对于高维系统或不同的淬灭协议也有效。在必须采取额外步骤来计算自旋极化{}的情况下,这种非绝热特性为检测拓扑不变量提供了{}方案。{通过研究3D拓扑相的缓慢淬灭动力学,我们发现我们的发现不限于与时间成反比的逆向淬灭协议下的1D和2D拓扑相,而且对于高维系统或不同的淬灭协议也有效。
更新日期:2020-09-22
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