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arXiv 1806.06976hep-thcond-mat.str-el
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有限密度下Chern-Simons物质理论中的旋-声子激发

Roton-phonon excitations in Chern-Simons matter theory at finite density

S. Prem Kumar, Dibakar Roychowdhury, Stanislav Stratiev

摘要:

本文考虑在严格零温度和有限化学势下,整体U(1)B粒子数或味对称的SU(N)Chern-Simons理论与标量场的耦合.在半经典的制度,我们确定了玻色凝聚基态的真空期望值(VEV)的标量伴随着非对易的背景规范场矩阵VEVs。这些矩阵与阿贝尔量子霍尔矩阵模型的液滴基态相一致。基态自发破缺U(1)_B,Higgses规范群,同时保持空间旋转和色味锁定的整体U(1)对称性。我们计算了SU(2)理论的半经典涨落的微扰谱,并证明了存在一个具有线性声子色散关系和决定Landau临界超流速度的旋子最小值(和最大值)的无质量单态.对于自相互作用为零的无质量标量理论,半经典色散关系和旋子极值的位置具有普遍的形式。

英文摘要:

We consider SU(N) Chern-Simons theory coupled to a scalar field in the fundamental representation at strictly zero temperature and finite chemical potential for the global U(1)_B particle number or flavour symmetry. In the semiclassical regime we identify a Bose condensed ground state with a vacuum expectation value (VEV) for the scalar accompanied by noncommuting background gauge field matrix VEVs. These matrices coincide with the droplet ground state of the Abelian quantum Hall matrix model. The ground state spontaneously breaks U(1)_B and Higgses the gauge group whilst preserving spatial rotations and a colour-flavour locked global U(1) symmetry. We compute the perturbative spectrum of semiclassical fluctuations for the SU(2) theory and show the existence of a single massless state with a linear phonon dispersion relation and a roton minimum (and maximum) determining the Landau critical superfluid velocity. For the massless scalar theory with vanishing self interactions, the semiclassical dispersion relations and location of roton extrema take on universal forms.

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