Details
| Original language | English |
|---|---|
| Article number | 085143 |
| Journal | Physical Review B |
| Volume | 106 |
| Issue number | 8 |
| Publication status | Published - 31 Aug 2022 |
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.
ASJC Scopus subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Physical Review B, Vol. 106, No. 8, 085143, 31.08.2022.
Research output: Contribution to journal › Article › Research › peer review
}
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 -