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