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In this paper prof. Wen states that (p.6)

a spontaneous higher symmetry broken state always corresponds to a topologically ordered state.

Are there examples of simple (or not) quantum spin models without any relation to topological order that can display this phenomenon? And what is the restriction in first place that does not allow non-topological states to have spontaneous higher symmetry broken states?

As a follow-up: do we know of any models that have spontaneous breaking of emergent (higher or not) fusion categorical symmetries?

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  • $\begingroup$ would you be content with quantum field theories (and not lattice/spin models) that exhibit these behaviours? $\endgroup$
    – ɪdɪət strəʊlə
    Commented Jun 19, 2023 at 18:32
  • $\begingroup$ Not 100%, but that would be a very good starting point if you have anything in mind. Or any citation... $\endgroup$
    – Kostas
    Commented Jun 19, 2023 at 19:07
  • $\begingroup$ What definition of spontaneous higher symmetry breaking do you want to use? $\endgroup$
    – Ruben Verresen
    Commented Jun 19, 2023 at 22:05
  • $\begingroup$ @Ruben From the point you define what a higher symmetry is (anomalous or not), I thought that the meaning of SHSB is unambiguous... Are there multiple definitions of it? In any case, I have in mind the definitions of p.4 of the same paper. $\endgroup$
    – Kostas
    Commented Jun 20, 2023 at 8:34

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