Operational definition of topological order

verfasst von
Amit Jamadagni, Hendrik Weimer
Abstract

The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase transitions. In particular, topological phase transitions cannot be characterized in terms of local order parameters, as it is the case with conventional symmetry-breaking phase transitions. Currently, topological order is mostly discussed in the context of nonlocal topological invariants or indirect signatures like the topological entanglement entropy. However, a comprehensive understanding of what actually constitutes topological order enabling precise quantitative statements is still lacking. Here we show that one can interpret topological order as the ability of a system to perform topological error correction. We find that this operational approach corresponding to a measurable quantity both lays the conceptual foundations for previous classifications of topological order and also leads to a successful classification in the hitherto inaccessible case of topological order in open quantum systems. We demonstrate the existence of topological order in open systems and their phase transitions to topologically trivial states. Our results demonstrate the viability of topological order in nonequilibrium quantum systems and thus substantially broaden the scope of possible technological applications.

Organisationseinheit(en)
Institut für Theoretische Physik
QuantumFrontiers
SFB 1227: Designte Quantenzustände der Materie (DQ-mat)
Typ
Artikel
Journal
Physical Review B
Band
106
ISSN
2469-9950
Publikationsdatum
31.08.2022
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Elektronische, optische und magnetische Materialien, Physik der kondensierten Materie
Elektronische Version(en)
https://doi.org/https://arxiv.org/abs/2005.06501 (Zugang: Offen)
https://doi.org/10.1103/PhysRevB.106.085143 (Zugang: Geschlossen)