标题： 非晶分数量子霍尔效应的耦合线构造 显示英文标题

标题： Coupled-wire Construction of a Non-crystalline Fractional Quantum Hall Effect

摘要： 分数量子霍尔效应，一种具有典型拓扑有序状态的现象，在二维强相关量子气体和晶体的陈绝缘体带中得到了实现。 在这里，我们通过耦合在实空间中非周期性放置的量子线来构建一个非晶态类似物。 值得注意的是，该模型使用玻色化技术仍然可解。 由于导线之间的非均匀耦合，基态的简并度与晶体情况不同。 它展示了激发态丰富的现象学，这些激发态可以表现为局限于一维运动的任意子（线离子），局限于在两条导线之间跳跃的任意子（s-线离子），以及可以在整个系统中自由移动的任意子激发。 基态的简并度和任意子统计直接由导线在实空间中的位置决定。 通过提供一个非晶态分数量子霍尔效应的解析可解模型，我们的工作展示了拓扑序可以在晶体之外展示更丰富的现象学。 更广泛地说，我们开发的非均匀导线构造可以作为探索非晶态系统中更丰富的多体现象学的工具。 显示英文摘要

摘要： The fractional quantum Hall effect, a paradigmatic topologically ordered state, has been realised in two-dimensional strongly correlated quantum gases and Chern bands of crystals. Here we construct a non-crystalline analogue by coupling quantum wires that are not periodically placed in real-space. Remarkably, the model remains solvable using bosonisation techniques. Due to the non-uniform couplings between the wires, the ground state has different degeneracy compared to the crystalline case. It displays a rich phenomenology of excitations, which can either behave like anyons confined to move in one dimension (lineons), anyons confined to hop between two wires (s-lineons), and anyonic excitations that are free to travel across the system. Both the ground state degeneracy and mutual statistics are directly determined by the real-space positions of the wires. By providing an analytically solvable model of a non-crystalline fractional quantum Hall effect, our work showcases that topological order can display richer phenomenology beyond crystals. More broadly, the non-uniform wire construction we develop can serve as a tool to explore richer many-body phenomenology in non-crystalline systems.