Abstract
AbstractRealizing 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.
Funder
Gordon and Betty Moore Foundation
National Science Foundation
Publisher
Springer Science and Business Media LLC
Reference50 articles.
1. Wen, X.-G. Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, 2007). https://doi.org/10.1093/acprof:oso/9780199227259.001.0001.
2. Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).
3. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Modern Phys. 80, 1083–1159 (2008).
4. Samajdar, R., Ho, W. W., Pichler, H., Lukin, M. D. & Sachdev, S. Quantum phases of Rydberg atoms on a kagome lattice. Proc. Natl Acad. Sci. 118, e2015785118 (2021).
5. Verresen, R., Lukin, M. D. & Vishwanath, A. Prediction of Toric Code Topological Order from Rydberg Blockade. Phys. Rev. X 11, 031005 (2021).