Liu Shang
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, USA.
Nat Commun. 2024 Jun 15;15(1):5134. doi: 10.1038/s41467-024-47856-7.
Realizing topological orders and topological quantum computation is a central task of modern physics. An important but notoriously hard question in this endeavor is how to diagnose topological orders that lack conventional order parameters. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to detect nontrivial topological order from a ground state wave function, but is far from enough for fully determining the topological order. In this work, we take a key step further in this direction: We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. The choice of the space manifold and the ground state is arbitrary. This protocol is both validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.
实现拓扑序和拓扑量子计算是现代物理学的核心任务。在这一努力过程中，一个重要但极其困难的问题是如何诊断缺乏传统序参量的拓扑序。这一问题的一个突破是拓扑纠缠熵的发现，它可用于从基态波函数中检测非平凡拓扑序，但对于完全确定拓扑序来说还远远不够。在这项工作中，我们在这个方向上又迈出了关键一步：我们提出了一个基于纠缠的简单方案，用于从二维中的单个基态波函数提取所有任意子的量子维度。空间流形和基态的选择是任意的。该方案在连续统中得到了验证，在晶格上也得到了检验，并且我们预计它在各种量子模拟平台上都可实现。
