Sufficient symmetry conditions for Topological Quantum Order

Details Sufficient symmetry conditions for Topological Quantum Order Sufficient symmetry conditions for Topological Quantum Order

2006-05-12

arxiv.org/abs/cond-mat/0605316v2

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages

Scientific paper

10.1073/pnas.0803726105

We prove sufficient conditions for Topological Quantum Order (TQO). The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (GLSs), thus providing a unifying framework based on a symmetry principle. All known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of GLSs (including topological terms and charges) and, most importantly, show the insufficiency of the energy spectrum, (recently defined) entanglement entropy, maximal string correlators, and fractionalization in establishing TQO. Duality mappings illustrate that not withstanding the existence of spectral gaps, thermal fluctuations can impose restrictions on suggested TQO computing schemes. Our results allow us to go beyond standard topological field theories and engineer new systems with TQO.

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