论文标题

一维相互作用的拓扑绝缘子中的准粒子激发:基于掺杂剂的量子模拟应用

Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation

论文作者

Mikhail, David, Voisin, Benoit, Medar, Dominique Didier St, Buchs, Gilles, Rogge, Sven, Rachel, Stephan

论文摘要

我们研究了电子电子相互作用对跨度Su-Schrieffer-Heeger(SSH)模型的电荷激发光谱的影响,这是1D散装阻塞拓扑绝缘子的原型。考虑到基于掺杂剂的量子模拟器制造的最新进展,我们着重于有限晶格中相互作用拓扑的实验可检测到的特征。为此,我们使用基于Lanczos的精确对角线化来计算真实空间中的单粒子光谱函数,从而将状态的局部密度推广到相互作用系统。它的空间和光谱分辨率允许直接研究边缘状态。通过研究非相互作用的极限,我们证明了边界上的拓扑内间隙状态与有限尺寸效应以及随机键和现场障碍相当强大,这表明在硅的工程掺杂阵列中模拟SSH模型的可行性。尽管对于任何有限的相互作用强度,但边缘激发变为零能旋转,但我们对光谱函数的分析表明,单粒子电荷激发被散布在边界上。尽管缺失了拓扑保护,但我们发现这些边缘激发像准颗粒一样长,只要它们留在散装间隙内。在$ u_c \ \ 5 t $的临界相互作用强度之上,这些准粒子在边界上的这些准颗粒松动它们的连贯性,这是通过边缘和散装状态的合并来解释的。这与文献中建立的强耦合极限的多体边缘激发相反。我们的发现表明,对于中等排斥性相互作用,可以使用单粒子局部测量技术(例如扫描隧道谱图)来检测相互作用SSH模型的非平凡阶段。

We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a 1D bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the non-interacting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spin-like for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection we find that these edge excitations are quasiparticle-like as long as they remain within the bulk gap. Above a critical interaction strength of $U_c\approx 5 t$ these quasiparticles on the boundary loose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the non-trivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.

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