Emergent (2+1)D topological orders from iterative (1+1)D gauging
1University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria. jgarrerubio@gmail.com.
Nature Communications
|September 12, 2024
Summary
This study introduces a novel method for creating topological quantum codes by iteratively gauging symmetries on spin chains. This approach generates codes that confine anyons and can be extended to higher dimensions, revealing gapped boundaries and tensor network representations.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- High Energy Physics
Background:
- Gauging localizes global symmetries, introducing dual symmetries on gauge fields.
- Iterative gauging on spin chains with Abelian symmetries forms the XZZX-code stabilizer.
Purpose of the Study:
- To develop a method for constructing topological quantum codes with confined anyons.
- To explore the relationship between gauging, anyon confinement, and topological phases.
- To establish a route for generating higher-dimensional topological codes and identifying their boundaries.
Main Methods:
- Iterative gauging of global symmetries on spin chains with Abelian group symmetries.
- Arranging gauge fields in a 2D lattice to form local symmetries.
- Twisting the gauging map to create codes that confine anyons.
Main Results:
- Local symmetries stabilize the XZZX-code for any Abelian group.
- Twisted gauging yields codes confining anyons with specific operator violations.
- Fusion of anyons results in mobile dipole or immobile Sierpiński-like excitations.
- Construction naturally realizes gapped boundaries from (1+1)D systems.
- Method provides a route to higher-dimensional topological codes and their boundary/tensor network representations.
Conclusions:
- The iterative gauging method provides a systematic construction for topological codes with confined anyons.
- This framework unifies concepts from symmetry gauging, topological phases, and quantum error correction.
- The approach offers new insights into the structure of topological codes, their boundaries, and their realization in physical systems.
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