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The conventional superfluid phase in a Bose-Hubbard ground state has $U(1)$ symmetry. In the presence of spin-orbit coupling (SOC), the superfluid ground state has non-uniform phases. Why do people in literature often say SOC breaks the $U(1)$ symmetry of superfluid?

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  • $\begingroup$ Which literature? $\endgroup$
    – Qmechanic
    Commented Aug 10, 2015 at 19:38
  • $\begingroup$ @Qmechanic In this review articel about Spint-Orbit coupled quantum gas arxiv.org/abs/1110.6798 $\endgroup$
    – rain
    Commented Aug 10, 2015 at 20:12
  • $\begingroup$ Superfluid by definition spontaneously breaks $\mathrm{U}(1)$ of particle-number conservation. That does not change when you add SOC. $\endgroup$
    – Meng Cheng
    Commented Aug 10, 2015 at 21:06

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