Topologically-ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Their preparation requires thus a precise fine tunning of the system’s parameters, a very challenging task in most experimental setups. In this work, we investigate a model of spinless fermions interacting with dynamical ${\mathbb{Z}}_2$ gauge fields on a cross-linked ladder, and show evidence of topological order throughout the full parameter space. In particular, we show how a magnetic flux is spontaneously generated through the ladder due to an Aharonov-Bohm instability, giving rise to topological order even in the absence of a plaquette term. Moreover, the latter coexists here with a symmetry-protected topological phase in the matter sector, that displays fractionalised gauge-matter edge states, and intertwines with it by a flux-threading phenomenon. Finally, we unveil the robustness of these features through a gauge frustration mechanism, akin to geometric frustration in spin liquids, allowing topological order to survive to arbitrarily large quantum fluctuations. In particular, we show how, at finite chemical potential, topological solitons are created in the gauge field configuration, which bound to fermions forming ${\mathbb{Z}}_2$ deconfined quasi-particles. The simplicity of the model makes it an ideal candidate where 2D gauge theory phenomena, as well as exotic topological effects, can be investigated using cold-atom quantum simulators.

中文翻译：

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Fermionicℤ2Gauge理论中的稳健拓扑顺序：从Aharonov-Bohm不稳定性到孤子诱导的去约束

物质的拓扑有序相虽然可以抵抗局部扰动，但在相图中通常局限于相对较小的区域。因此，他们的准备工作需要对系统参数进行精确的微调，这在大多数实验设置中都是一项非常艰巨的任务。在这项工作中，我们研究了无旋费米子与动力相互作用的模型${\mathbb{Z}}_2$在交联的阶梯上测量场，并在整个参数空间中显示拓扑顺序的证据。特别是，我们展示了由于Aharonov-Bohm不稳定性，如何通过梯子自发地产生磁通量，即使在没有褶皱项的情况下也产生拓扑次序。此外，后者在此与物质扇区中受对称保护的拓扑相共存，该拓扑相显示分数尺度的质子边缘状态，并通过磁通量缠结现象交织在一起。最后，我们通过标准的挫折机制揭示了这些功能的稳健性，类似于自旋液体中的几何挫折，从而允许拓扑顺序得以生存，以承受任意大的量子涨落。特别是，我们展示了如何在有限的化学势下${\mathbb{Z}}_2$解禁准粒子。该模型的简单性使其成为使用冷原子量子模拟器可以研究二维规范理论现象以及奇异拓扑效应的理想选择。