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arXiv 2511.08053cond-mat.mes-hall
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开放准周期梯子中的局域化转变

Localization transitions in an open quasiperiodic ladder

Suparna Sarkar, Soumya Satpathi, Swapan K. Pati

AI总结:

本研究针对Aubry-André-Harper模型描述的开放准周期梯子,利用Liouvillian超算符与非厄米哈密顿量的对应关系,发现一维近邻系统中耗散可诱导混合相区,且其临界点和窗口宽度可通过耗散强度调节。

摘要:

我们研究了开放准周期梯子中的局域化转变,其中准周期性由Aubry-André-Harper模型描述。虽然先前的研究表明高阶跳跃或受约束的准周期势可以在一维系统中诱导混合相区,但我们证明,在不对准周期势或跳跃参数施加任何显式约束的一维近邻系统中,耗散可以诱导混合相区。我们的方法利用了Liouvillian超算符的本征谱与非厄米哈密顿量的本征谱之间的精确对应关系,这对线性耗散下的二次费米子系统有效。使用Majorana费米子表示中的三次量子化方法,我们分析了两种耗散配置:每个位点交替增益和损耗,以及交替位点在平衡和不平衡条件下的情况。通过计算逆参与率和归一化参与率,我们表明耗散可以驱动系统进入三个不同的相:非局域化相、混合相和局域化相。值得注意的是,每个位点的平衡耗散不存在混合相区,但引入不平衡后会出现;而对于交替位点耗散,平衡和不平衡情况下均会出现混合相区。此外,通过改变耗散强度可以选择性地调节临界点和混合相窗口的宽度。这些发现揭示了耗散在重塑准周期系统中的局域化转变方面起着决定性作用,为非厄米效应与准周期有序之间的相互作用提供了新的见解。

英文摘要:

We investigate localization transition in an open quasiperiodic ladder where the quasiperiodicity is described by the Aubry-André-Harper model. While previous studies have shown that higher-order hopping or constrained quasiperiodic potentials can induce a mixed-phase zone in one dimension, we demonstrate that the dissipation can induce mixed phase zone in a one dimensional nearest-neighbor system without imposing any explicit constraints on the quasiperiodic potential or hopping parameter. Our approach exploits an exact correspondence between the eigenspectrum of the Liouvillian superoperator and that of the non-Hermitian Hamiltonian, valid for quadratic fermionic systems under linear dissipation. Using third quantization approach within Majorana fermionic representation, we analyze two dissipation configurations: alternating gain and loss at every site, and at alternate sites under balanced and imbalanced conditions. By computing the inverse and normalized participation ratios, we show that dissipation can drive the system into three distinct phases: delocalizd, mixed, and localized. Notably, the mixed-phase zone is absent for balanced dissipation at every site but emerges upon introducing imbalance, while for alternate site dissipation it appears in both balanced and imbalanced cases. Furthermore, the critical points and the width of the mixed-phase window can be selectively tuned by varying the dissipation strength. These findings reveal that the dissipation plays a decisive role in reshaping localization transitions in quasiperiodic systems, offering new insight into the interplay between non-Hermitian effects and quasiperiodic order.

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