Critical exponents of the nonlinear sigma model on a Grassmann manifold U(N)/U(m)U(N - m) by the 1/N-expansion
Critical exponents of the nonlinear sigma model on a Grassmann manifold U(N)/U(m)U(N - m) by the 1/N-expansion
复制标题
格拉斯曼流形 U(N)/U(m)U(N - m) 上非线性 sigma 模型的 1/N 展开的临界指数
DOI：
10.1103/physrevb.99.165142
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发表时间：
2019
影响因子：
3.7
通讯作者：
Wang Qiang-Hua
中科院分区：
文献类型：
--
作者：
Wang Shan-Yue;Wang Da;Wang Qiang-Hua
受冷原子物理学中SU（N）反铁磁性的多行表示实现的启发，我们利用复射影表示研究了定义在Grassmann流形U（N）/U（m）U（N-m）上的SU（N）反铁磁性的低能非线性sigma模型，它是广泛研究的CPN-1模型（对应于m = 1）的直接推广.使用大N展开到1/N的一阶，固定in，在空间维度2 < d < 4中，我们获得了临界指数，特别是与实验测量直接相关的规范无关指数。发现这些指数仅依赖于rn/N，表明较大的rn有效地减少N，从而引起鞍点附近的更强的波动。
Motivated by the realization of SU(N) antiferromagnetism with the multirow representations in coldatom physics, we studied its low-energy nonlinear sigma model defined on the Grassmann manifold U(N)/U(m)U(N - m) using the complex projective presentation, which is a direct generalization of the widely studied CPN-1 model (corresponding to m = 1). Using the large-N expansion up to the first order of 1/N with fixed in, and in space dimension 2 < d < 4, we obtain the critical exponents, including in particular the gauge-independent exponents that are directly relevant for experimental measurements. These exponents are found to depend only on rn/N, indicating that a larger rn effectively reduces N and thus causes stronger fluctuations about the saddle point.