in a paper http://arxiv.org/abs/1011.2273 there is a possibility shown that gapped modes at edges can exist for non-trivial interacting topological systems and mathematically shown that gapless modes get replaced by zero's of green's function, I don't understand what does zero of Green's function represent ? and Is it really possible to have gapped modes for interacting non-trivial topological systems because for non-trivial topological systems there are always gapless edges modes present

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    $\begingroup$ Zero of Green's function mean that there is no quasiparticle anymore. It is no longer a good picture to think about weakly interacting fermions. In this example, when the edge modes become gapped (without breaking symmetry), it means the system is NOT topological. $\endgroup$ – Meng Cheng Jun 18 '15 at 20:43
  • $\begingroup$ @MengCheng so does it mean that we can have topological phase transition between two different topological systems without closing band gap? $\endgroup$ – user48826 Jun 18 '15 at 20:53
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    $\begingroup$ If the gap does not close, then it is not a phase transition. The point is that these are the same topological phase even though they are classified as being different when the system is not interacting. $\endgroup$ – Meng Cheng Jun 18 '15 at 22:04

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