We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks-Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids,we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases.

中文翻译：

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被困 Lieb-Liniger 任意离子气体的单粒子密度矩阵

我们利用空间非均匀量子系统的场论描述的最新进展，提供了在一维中被困相互作用的任意子气体的零温度单粒子密度矩阵的全面表征。我们首先重新审视具有逐点相互作用的均质任意子气体。在有限相互作用强度的单粒子密度矩阵的谐波 Luttinger 液体膨胀中，非通用场振幅尚不清楚。我们从场形状因子的 Bethe Ansatz 公式中提取它们，提供此相关函数的精确渐近展开，从而扩展了 Tonks-Girardeau 极限中的可用结果。接下来，我们用非平凡的密度分布分析被困气体。通过对非均匀 Luttinger 液体应用最新的分析和数值技术，我们为单粒子密度矩阵提供了精确的扩展。我们展示了不同限制势的结果，强调了玻色气体的主要差异。