磁子的高自旋理论
Higher-Spin Theory of the Magnetorotons
摘要：
分数量子霍尔液体表现出丰富的激发，其中能量最低的是在有限动量的色散最小的磁子。我们提出了一个理论上的量子霍尔高原近半填充，即在填充分数$ν=N/(2N+1)$在大$N$的磁振子。该理论涉及无限数量的玻色场所产生的玻色化的波动的形状的复合费米面。在零动量时，有$O(N)$中性激发，每一个都携带一个运行整数值$2,3,\ldots$的明确定义的自旋。在非零动量$q$的模式的混合导致的最低激发和磁子极小值的外观的特征向下弯曲。一个纯粹的代数参数表明，磁子最小值位于$q\ell_B=z_i/(2N+1)$，其中$\ell_B$是磁长度和$z_i$是贝塞尔函数$J_1$的零，独立的微观细节。我们认为，这些极小值是任何二维费米面耦合到规范场在一个小的背景磁场的普遍特征。
英文摘要：
Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions $ν=N/(2N+1)$ at large $N$. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are $O(N)$ neutral excitations, each carrying a well-defined spin that runs integer values $2,3,\ldots$. The mixing of modes at nonzero momentum $q$ leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at $q\ell_B=z_i/(2N+1)$, where $\ell_B$ is the magnetic length and $z_i$ are the zeros of the Bessel function $J_1$, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.
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