• DOI:10.1103/PhysRevB.93.205112
• Corpus ID: 119556783

Robust Topological Degeneracy of Classical Theories

@article{Vaezi2015RobustTD,
  title={Robust Topological Degeneracy of Classical Theories},
  author={Mohammad-Sadegh Vaezi and Gerardo Guzman Ortiz and Zohar Nussinov},
  journal={Physical Review B},
  year={2015},
  volume={93},
  pages={205112}
}

• Mohammad-Sadegh Vaezi, G. Ortiz, Z. Nussinov
• Published 24 November 2015
• Physics, Mathematics
• Physical Review B

We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display non-local entanglement. To this end, we introduce and study a classical rendition of the Toric Code model embedded on Riemann surfaces of different genus numbers. We find that the minimal ground state degeneracy (and those of all levels) depends on the topology of the embedding surface alone. As the ground states of this classical system may be distinguished by local measurements, a characteristic of Landau orders, this example illustrates that topological degeneracy is not a sufficient condition for topological quantum order. This conclusion is generic and, as shown, it applies to many other models. We also demonstrate that certain lattice realizations of these models, and other theories, display a ground state entropy (and those of all levels) that is "holographic", i.e., extensive in the system boundary. We find that clock and $U(1)$ gauge theories display topological (in addition to gauge) degeneracies.