Volume 113, Number 5, March 2016
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||18 March 2016|
Topological and error-correcting properties for symmetry-protected topological order
1 Department of Mathematics & Statistics, University of Guelph - Guelph, Ontario, Canada
2 Institute for Quantum Computing, University of Waterloo - Waterloo, Ontario, Canada
3 Canadian Institute for Advanced Research - Toronto, Ontario, Canada
4 Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences Beijing 100190, China
Received: 17 November 2015
Accepted: 6 March 2016
We study the symmetry-protected topological (SPT) orders for bosonic systems from an information-theoretic viewpoint. We show that with a proper choice of the onsite basis, the degenerate ground-state space of SPT orders (on a manifold with boundary) is a quantum error-correcting code with macroscopic classical distance, hence is stable against any local bit-flip errors. We show that this error-correcting property of the SPT orders has a natural connection to that of the symmetry-breaking orders, whose degenerate ground-state space is a classical error-correcting code with a macroscopic distance, providing a new angle for the hidden symmetry-breaking properties in SPT orders. We further propose new types of topological entanglement entropy that probe the SPT orders hidden in their symmetric ground states, which also signal the topological phase transitions protected by symmetry. Combined with the original definition of topological entanglement entropy that probes the “intrinsic topological orders”, and the recent proposed one that probes the symmetry-breaking orders, the set of different types of topological entanglement entropy may hence distinguish topological orders, SPT orders, and symmetry-breaking orders, which may be mixed up in a single system.
PACS: 64.70.Tg – Quantum phase transitions / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 03.67.Pp – Quantum error correction and other methods for protection against decoherence
© EPLA, 2016
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