论文标题

部分可观测时空混沌系统的无模型预测

Emergent $U(1)$ Symmetries and $τ$-$σ$ Duality in Gapless Superfluids or Superconductors

论文作者

Zhou, Fei

论文摘要

超流体自发地破坏了通常的$ u(1)$对称性,因为凝结。在本文中,我们说明了六类新兴$ u(1)$对称性自然出现在一系列无间隙拓扑超级流体(属于稳定阶段,或者是量子关键的)中。在我们考虑过的无间隙状态下,紧急$ u(1)$对称组嵌入到$ spin(4)= su(2)\ otimes su(2)$ group中,该组为$ SO(4)$组。在$ su(2)$ spin组或相当于它的情况下,与对称性相关的所有$ u(1)$费用是进一步不变的,但总是会破坏较高的时空lorentz对称$ so(3,1)$ group。仅当相互作用足够强,并且由此产生的强耦合状态完全散布时,即将出现的$ u(1)$对称性才能自发地破坏。但是,如果状态保持无间隙,尽管这些状态与弱相互作用的无间隙Lorentz对称柜台零件相比,这些状态可能表现出更低的时空对称性,但始终存在$ U(1)$ u(1)$对称性。在我们的利益方面,我们已经确定了有或没有Lorentz对称性的所有可能的无间隙的真实费物,发现它们都以红外极限显示出来的$ U(1)$对称性。我们认为,在互动的超高范围内,相互交互的超级固定在互动的超高范围内,并且在互动的范围内是固有的,并且是典型的,并且是超高的,并且是超高的,并且是超高的,并且是超高的,并且是超高的,并且是超高的,并且是超级良好的范围。红外稳定固定点决定了新兴特性。

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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