我们推导出了在强耦合和弱耦合情况下一维$κ$ -分量费米子的Fredholm方程的渐近展开式的前几项。因此，我们得到了一个高精度的结果，基态能量的多组分费米气体与极化这些制度。这一结果为具有更高自旋对称性的费米气体的基态性质提供了统一的描述。然而，与双组分费米气体相比，当相互作用强度为零时，不存在可以统一两组Fredholm方程的映射。此外，我们发现局域对关联函数揭示了$κ$ -分量相互作用费米子的量子统计效应。对于具有排斥相互作用的平衡自旋情形，所得到的基态能量证实了Yang和You的结果[Chin. Phys. Lett. { \bf 28}，020503（2011）]，每个粒子的能量作为$κ\to \infty$与无自旋玻色子相同。
英文摘要：
We derive the first few terms of the asymptotic expansion of the Fredholm equations for one-dimensional $κ$-component fermions with repulsive and with attractive delta-function interaction in strong and weak coupling regimes. We thus obtain a highly accurate result for the ground state energy of a multicomponent Fermi gas with polarization for these regimes. This result provides a unified description of the ground state properties of the Fermi gas with higher spin symmetries. However, in contrast to the two-component Fermi gas, there does not exist a mapping that can unify the two sets of Fredholm equations as the interacting strength vanishes. Moreover, we find that the local pair correlation functions shed light on the quantum statistic effects of the $κ$-component interacting fermions. For the balanced spin case with repulsive interaction, the ground state energy obtained confirms Yang and You's result [Chin. Phys. Lett. {\bf 28}, 020503 (2011)] that the energy per particle as $κ\to \infty$ is the same as for spinless Bosons.
Generalized Effective Spin-Chain formalism for multicomponent anyons in one-dimensional optical lattices
Rice University（莱斯大学）；The University of Oklahoma（俄克拉荷马大学）；Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院）；Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院）
