Title: Correlations in Disordered Solvable Tensor Network States Show Chinese title

Title: 无序可解张量网络态中的关联性

Abstract: Solvable matrix product and projected entangled pair states evolved by dual and ternary-unitary quantum circuits have analytically accessible correlation functions. Here, we investigate the influence of disorder. Specifically, we compute the average behavior of a physically motivated two-point equal-time correlation function with respect to random disordered solvable tensor network states arising from the Haar measure on the unitary group. By employing the Weingarten calculus, we provide an exact analytical expression for the average of the $k$th moment of the correlation function. The complexity of the expression scales with $k!$ and is independent of the complexity of the underlying tensor network state. Our result implies that the correlation function vanishes on average, while its covariance is nonzero. Show Chinese abstract

Abstract: 可解矩阵乘积和由双元和三元酉量子电路演化的投影纠缠对态具有解析可访问的相关函数。 在这里，我们研究无序的影响。 具体来说，我们计算一个物理上有意义的两点等时相关函数在来自酉群上哈尔测度的随机无序可解张量网络态下的平均行为。 通过使用 韦因加滕微积分，我们提供了相关函数的$k$阶矩的平均值的精确解析表达式。 该表达式的复杂度与$k!$相关，并且与底层张量网络态的复杂度无关。 我们的结果表明，相关函数在平均意义上消失，而其协方差不为零。