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Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st column) and in other lecture slides (page 6 of http://discor2013.files.wordpress.com/2013/12/lee.pdf). This slide appears to talk about some mean field result of spin liquid state.

This statement is not really pertinent to the mainstream of that paper. But it sounds rather intriguing and necessary to be further clarified. So could anyone make it clearer? Thanks!

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    $\begingroup$ Could you please provide a reference? $\endgroup$
    – Frederic Brünner
    Commented Jul 31, 2014 at 8:11
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    $\begingroup$ Reference updated. $\endgroup$
    – xiaohuamao
    Commented Jul 31, 2014 at 8:40
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    $\begingroup$ Since this paper is not so old, perhaps it is worth asking to the authors directly, and then give us their answer :-) $\endgroup$
    – FraSchelle
    Commented Sep 13, 2014 at 10:05
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    $\begingroup$ Related: physics.stackexchange.com/questions/75856/… $\endgroup$
    – Clever
    Commented Feb 1, 2015 at 10:32

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I met the author of that paper today. He said it's more of an empirical observation rather than a statement based on solid arguments. He asked for a counterexample, which I don't have. Please post it here once you got one.

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The statement is not true. Counter example: quantum spin ice or U(1) spin liquid. In gapless spin liquid phase, the boson (spin excitations) are emergent U(1) photons in the deconfined phase, which are gapless but not condensed.

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    $\begingroup$ Thanks! Where can I find any reference? $\endgroup$
    – xiaohuamao
    Commented Apr 19, 2015 at 1:20

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