论文标题
可集成XXZ链和本地扰动的量子chaotic xxz链中的异分基矩阵元素的低频行为
Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
论文作者
论文摘要
我们研究了可集成XXZ链的本征状态的本地操作员的矩阵元素以及通过局部用磁性杂质局部扰动XXZ链获得的量子差模型的基质元素。我们表明，在系统尺寸中多项式较小的频率下，根据操作员的不同，异基矩阵元素方差的行为可能截然不同。在可集成的模型中，我们发现，作为频率$ω\ rightarrow0 $，方差要么是非趋势（通用行为）或消失的（对于特殊的操作员）。另一方面，在量子 - 偶然模型中，我们发现这些方差为$ω\ rightarrow0 $，并指示扩散动力学。我们强调了本地运算符的矩阵元素的哪些属性在可独立于所选的特定运算符的集成和量子 - 偶然模型之间有所不同。
We study the matrix elements of local operators in the eigenstates of the integrable XXZ chain and of the quantum-chaotic model obtained by locally perturbing the XXZ chain with a magnetic impurity. We show that, at frequencies that are polynomially small in the system size, the behavior of the variances of the off-diagonal matrix elements can be starkly different depending on the operator. In the integrable model we find that, as the frequency $ω\rightarrow0$, the variances are either nonvanishing (generic behavior) or vanishing (for a special class of operators). In the quantum-chaotic model, on the other hand, we find the variances to be nonvanishing as $ω\rightarrow0$ and to indicate diffusive dynamics. We highlight which properties of the matrix elements of local operators are different between the integrable and quantum-chaotic models independently of the specific operator selected.
