TY - JOUR

T1 - Operational definition of topological order

AU - Jamadagni, Amit

AU - Weimer, Hendrik

N1 - Funding Information: We thank S. Diehl and T. Osborne for fruitful discussions. This work was funded by the Volkswagen Foundation, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within SFB 1227 (DQ-mat, Project No. A04), SPP 1929 (GiRyd), and under Germany's Excellence Strategy – EXC-2123 QuantumFrontiers – 390837967.

PY - 2022/8/31

Y1 - 2022/8/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85137742949&partnerID=8YFLogxK

U2 - https://arxiv.org/abs/2005.06501

DO - https://arxiv.org/abs/2005.06501

M3 - Article

AN - SCOPUS:85137742949

VL - 106

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 8

M1 - 085143

ER -