热平衡中的一维不可穿透任意子。III。空间相关性的大距离渐近性
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
摘要：
利用前人得到的有限温度下不可穿透任意子的场-场关联函数的行列式表示，我们导出了一个完全刻画不可穿透任意子的非线性偏微分方程组.该系统与不可穿透玻色子的系统相同，但具有不同的初始条件。通过对微分方程组的Riemann-Hilbert问题的分析，得到了关联函数的大距离渐近性质。我们计算的指数和指数前因子的渐近的场-场耦合。在统计参数$κ$的适当极限$κ\to 1$和$κ\to 0$内，用这种方法导出的渐近性与自由费米子和不可穿透玻色子的渐近性一致，并且与低温下共形场论的预言一致。
英文摘要：
Using the determinant representation for the field-field correlation functions of impenetrable anyons at finite temperature obtained in a previous paper, we derive a system of nonlinear partial differential equations completely characterizing the correlators. The system is the same as the one for impenetrable bosons but with different initial conditions. The large-distance asymptotic behavior of the correlation functions is obtained from the analysis of the Riemann-Hilbert problem associated with the system of differential equations. We calculate both the exponential and pre-exponential factors in the asymptotics of the field-field correlators. The asymptotics derived in this way agree with those of the free fermions and impenetrable bosons in the appropriate limits, $κ\to 1$ and $κ\to 0$, of the statistics parameter $κ$, and coincide with the predictions of the conformal field theory at low temperatures.
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