Emergent $U(1)$ Symmetries and $\tau$-$\sigma$ Duality in Gapless
Superfluids or Superconductors
- URL: http://arxiv.org/abs/2208.10486v2
- Date: Thu, 6 Apr 2023 18:33:10 GMT
- Title: Emergent $U(1)$ Symmetries and $\tau$-$\sigma$ Duality in Gapless
Superfluids or Superconductors
- Authors: Fei Zhou
- Abstract summary: A superfluid spontaneously breaks the usual $U(1)$ symmetry because of condensation.
We show six classes of emergent $U(1)$ symmetries naturally appear in infrared limits in a broad class of gapless topological superfluids.
- Score: 5.647516208808728
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A superfluid spontaneously breaks the usual $U(1)$ symmetry because of
condensation. In this article, we illustrate six classes of emergent $U(1)$
symmetries naturally appear in infrared limits in a broad class of gapless
topological superfluids (that either belong to a stable phase or are quantum
critical). In gapless states we have considered, emergent $U(1)$ symmetry
groups are embedded in an $Spin(4)=SU(2) \otimes SU(2)$ group that are
algebraically isomorphic to an $SO(4)$ group. All $U(1)$ charges associated
with symmetries are further invariant under an $SU(2)$ spin group or an
equivalent of it but always break pre-existing higher space-time Lorentz
symmetry of $SO(3,1)$ group. Emergent $U(1)$ symmetries can be further
spontaneously broken only if interactions are strong enough and resultant
strong coupling states become fully gapped. However if states remain gapless,
emergent $U(1)$ symmetries are always present, despite that these states may
exhibit much lower space-time symmetries compared to their weakly interacting
gapless Lorentz symmetric counter parts. In the limit of our interests, we have
identified all possible gapless real fermions with or without Lorentz
symmetries and find that they all display emergent $U(1)$ symmetries in the
infrared limit.We argue emergent $U(1)$ symmetries in infrared are intrinsic in
a broad class of interacting gapless superfluid or superconducting states and
are typically well defined in high dimensions where there are infrared stable
fixed points dictating emergent properties.
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