Phase transitions in a non-Hermitian Aubry-André-Harper model
Phase transitions in a non-Hermitian Aubry-André-Harper model
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DOI：
10.1103/physrevb.103.054203
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发表时间：
2021-02
影响因子：
3.7
通讯作者：
S. Longhi
中科院分区：
文献类型：
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作者：
S. Longhi
Aubry-Andr‘e-Harper模型提供了一维晶格中非周期有序化的范例，显示出在准周期势振幅的有限临界值{V}_(C)$处的离域-局域化相变。在系统的动力学行为方面，当测量波包扩展的量子扩散指数时，相变是不连续的，在离域相$Vl{V}_{c}$(弹道传输)，$\ensureath{\Delta}=1$(弹道传输)，在临界点$V={V}_{c}$(扩散传输)，以及在定域相$VG{V}_{c}$(动态局域化)$\ensureath{\Delta}=0$。然而，当测量作为动力学变量的激发在晶格中传输的速度$v(V)$时，相变是光滑的，它是势幅$V$的连续函数，并且随着局域相的接近而消失。我们考虑了Aubry-Andr‘e-Harper模型的非厄米特推广，其中沿晶格的跳跃是不对称的，并且证明了动力学局域-离域转变是不连续的，不仅在扩散指数上是不连续的，而且在弹道传输的速度上也是不连续的。这意味着，即使非常接近光谱相变点，格子中也允许有限速度的弹道传输。此外，我们还证明了弹道速度可以随着$V增加到零以上而增加，也就是说，令人惊讶的是，晶格中的无序可以导致输运的增强。
The Aubry-Andr\'e-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value ${V}_{c}$ of the quasiperiodic potential amplitude $V$. In terms of the dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent $\ensuremath{\delta}$ of wave-packet spreading, with $\ensuremath{\delta}=1$ in the delocalized phase $Vl{V}_{c}$ (ballistic transport), $\ensuremath{\delta}\ensuremath{\simeq}1/2$ at the critical point $V={V}_{c}$ (diffusive transport), and $\ensuremath{\delta}=0$ in the localized phase $Vg{V}_{c}$ (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed $v(V)$ of excitation transport in the lattice, which is a continuous function of potential amplitude $V$ and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-Andr\'e-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous, not only in the diffusion exponent $\ensuremath{\delta}$, but also in the speed $v$ of ballistic transport. This means that even very close to the spectral phase transition point, rather counterintuitively, ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as $V$ is increased above zero, i.e., surprisingly, disorder in the lattice can result in an enhancement of transport.