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When I'm looking at descriptions of topological insulators, (non interacting just in case anybody ascribes interactions), I'm essentially looking at single particle quantum mechanics on a lattice.

What made quantum mechanics special to me was entanglement and measurement. If I were to force myself to only look at observables statistically (only expectation values) I would only be left with entanglement, hence non interacting systems(in this case the topological insulator) should have classical analogues, at least according to my reasoning.

Experimentally there are examples of photonic[1] and acoustic[2] topological insulators which support my arguments

If my understanding of quantum mechanics is correct, is there anything specifically special about what we understand of non-interacting Symmetry Protected Topological Phases (including the classification, etc) that would not be observed classically ? If it isn't what differentiates the materials called photonic and acoustic topological insulators from the quantum case?


[1] Khanikaev, Alexander B., et al. "Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials." arXiv preprint arXiv:1204.5700 (2012).

[2] He, Cheng, et al. "Acoustic topological insulator and robust one-way sound transport." arXiv preprint arXiv:1512.03273 (2015).

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Perhaps what makes these systems quantum is the fact that they must be Fermionic, and one must use the Pauli exclusion principle (an inherently quantum phenomenon) in order to fill the Fermi sea and get the Fermi projection. If it weren't for quantum mechanics, you wouldn't have such a Fermi projection and hence no topology. So in this sense you are taking interactions into account in the most primitive way: filling the Fermi sea.

The classical systems you cite are mere analogues of these quantum systems.

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  • $\begingroup$ this makes sense, I think if I find the exact areas where the analogy fails, I should be able to find the differences $\endgroup$ – Praharsh Suryadevara Dec 29 '16 at 13:17

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