论文标题
一维晶格中硬核Anyons的确切动力相关性
Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
论文作者
论文摘要
强相关系统的动态相关性是描述其非平衡性能的重要成分。我们提出了一种通用方法，可以准确计算一维晶格中硬核Anyons的动态相关性，对任何类型的限制电势和任何温度有效。我们获得了绿色功能，光谱函数和超时订购的相关器（OTOC）的精确表达。我们发现，Anyonic光谱函数显示了三个主要的奇异线线，可以将其解释为与Lieb-Liniger气体类似的双光谱。这些线的分散关系可以明确给出，它们以\ emph {hotpoint} $（q_m，ω_m）$跨越，该$（q_m，ω_m）$在$ q_m $ $ q_m $和本地频谱功能中的势力分配功能中诱导峰值，以$ω__m$ $ $ω_m$。我们还发现，任何人统计量可以在绿色的功能，频谱和OTOC中诱导空间不对称性。此外，以Otocs为特征的信息传播显示了轻锥动力学，一般统计和低温的不对称，但在无限温度下对称。我们的结果铺平了研究硬核Anyons的非平衡动力学的方法，并通过光谱函数在实验中探测任何统计量。
The dynamical correlations of a strongly correlated system is an essential ingredient to describe its non-equilibrium properties. We present a general method to calculate exactly the dynamical correlations of hard-core anyons in one-dimensional lattices, valid for any type of confining potential and any temperature. We obtain exact explicit expressions of the Green's function, the spectral function, and the out-of-time-ordered correlators (OTOCs). We find that the anyonic spectral function displays three main singularity lines which can be explained as a double spectrum in analogy to the Lieb-Liniger gas. The dispersion relations of these lines can be given explicitly and they cross at a \emph{hot point} $(q_m,ω_m)$, which induces a peak in the momentum distribution function at $q_m$ and a power-law singularity in the local spectral function at $ω_m$. We also find that the anyonic statistics can induces spatial asymmetry in the Green's function, its spectrum, and the OTOC. Moreover, the information spreading characterized by the OTOCs shows light-cone dynamics, asymmetric for general statistics and low temperatures, but symmetric at infinite temperature. Our results pave the way toward studying the non-equilibrium dynamics of hard-core anyons and experimentally probing anyonic statistics through spectral functions.
