论文标题
在Anyonic Lieb-Liniger模型中的野外形式的决定因素公式
Determinant formula for the field form factor in the anyonic Lieb-Liniger model
论文作者
论文摘要
我们在Anyonic Lieb-Liniger模型中得出了一个现场表格的确切公式，对交互$ c $，anyonic参数$κ$和粒子$ n $的任意值有效。类似于骨的情况，表现因素是按照$ n \ times n $矩阵的决定因素表示的，其元素是伯特质子的元素，但明确取决于$κ$。该公式可以有效评估，并为几个数值和分析计算提供了必不可少的成分。它的派生包括三个步骤。首先，我们表明，在标准Lieb-Liniger模型中，Anyonic外形效果等于两个特殊的脱壳状态之间的骨孔。其次，我们表征其分析属性，并提供一组唯一指定它的条件。最后，我们表明我们的行列式公式满足了这些条件。
We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction $c$, anyonic parameter $κ$, and number of particles $N$. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of a $N\times N$ matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on $κ$. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb-Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.
