混沌本征态中的三体纠缠

中文摘要 AI 辅助

现已公认，经典统计力学源于量子混沌系统的纠缠结构，这一点由（子系统）本征态热化假设（ETH）所量化。尽管这一论断基于此类系统本征态的双体纠缠（已被充分研究），但近年来的研究表明，多体态通常以多体纠缠为特征，由此引发一个问题：混沌本征态具有哪些普适的多体纠缠特征？我们通过两个三体纠缠探针——Rényi三体多熵和Rényi反射熵——的视角，研究遍历二分假设的三体推广，从而部分回答这一问题。我们利用鞍点分析推导出这两个量的系综平均的前导阶解析表达式。除这些度量外，我们还获得了控制Rényi-2反射熵的Rényi-2反射密度矩阵$\ ho_{AA^*}^{(2)}$的平均值。我们表明，混沌本征态中的$\ ho_{AA^*}^{(2)}$可由该系综平均很好地描述，与普通约化密度矩阵不同，它在子系统尺寸区间上呈现三种定性不同的形式，这可视为子系统ETH的三体推广。我们将解析预测与混合场Ising模型的精确对角化结果进行了基准比较。

英文摘要

It is now well-established that classical statistical mechanics emerges from the entanglement structure of quantum chaotic systems, as quantified by the (subsystem) eigenstate thermalization hypothesis (ETH). While this statement rests on the well-studied bipartite entanglement of the eigenstates of such systems, recent years have shown that many-body states are often characterized by multipartite entanglement, raising the question: what are the universal multipartite entanglement features of chaotic eigenstates? We answer this question in part by studying a tripartite generalization of the ergodic bipartition ansatz through the lens of two tripartite entanglement probes, the Rényi tripartite multi-entropy and the Rényi reflected entropy. We derive leading-order analytical expressions for the ensemble averages of both quantities using a saddle-point analysis. Beyond these measures, we obtain the average of the Rényi-2 reflected density matrix, $ρ_{AA^*}^{(2)}$,which controls the Rényi-2 reflected entropy. We show that $ρ_{AA^*}^{(2)}$ in a chaotic eigenstate is well-described by this ensemble average which, unlike an ordinary reduced density matrix, takes three qualitatively distinct forms across subsystem-size regimes, which may be viewed as a tripartite generalization of subsystem ETH. We benchmark our analytical predictions against exact diagonalization of the mixed-field Ising model.

发表机构

• Princeton University（普林斯顿大学）
• University of Chicago（芝加哥大学）

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