发表机构
Purdue University; University of Illinois at Urbana-Champaign; Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（普渡大学; 伊利诺伊大学厄巴纳-香槟分校; 斯坦福材料能源科学研究所，SLAC国家加速器实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出稳定化解析延拓方法，从整数阶Rényi熵重建冯·诺依曼熵，在多种多体系统中验证其性能，并揭示由Trρ^z零点导致的一阶Rényi相变机制。
AI 中文摘要
提取具有操作意义的信息量，如冯·诺依曼熵和互信息，是刻画多体量子系统的核心问题，然而实验和数值计算通常只能直接提供整数阶 Rényi 熵。传统的外推方法依赖于预设的拟合假设，而在 PRL 137, 100202 中，我们提出了一种基于稳定化解析延拓（SAC）的替代方法，该方法避免了此类假设，并且对噪声具有固有的鲁棒性。在此，我们进一步在无噪声环境下发展这一框架，并在多个非平凡的多体问题中对其性能进行基准测试。我们首先表明，除了从有限个 Rényi 样本重建冯·诺依曼熵的内在歧义外，解析延拓还可能因 Rényi 函数中由 $\ ext{Tr}\ ho^z$ 的零点引起的真正非解析性而失效。我们推导了 $\ ext{Tr}\ ho^z$ 的通用无零点区域，并利用关于 $\ ho$ 的额外谱信息系统地锐化这些界限。随后，我们在三种情形下对 SAC 的性能进行基准测试：（i）从环面码和 Kagome 海森堡模型的 DMRG Rényi 数据中提取拓扑纠缠熵；（ii）重建 $(1+1)d$ 紧致玻色子 CFT 中不相交区间之间的互信息；（iii）从整数阶 Rényi 熵恢复冯·诺依曼熵的有限时间弹道增长，这些熵在扩散量子动力学中交叉过渡到亚弹道增长。在后一种情形中，解析延拓预计在长时间极限下会失效。我们用一个具有物理动机的两扇区模型来说明这一机制，其中冯·诺依曼熵与高阶 Rényi 增长之间的渐近分离伴随着 $\ ext{Tr}\ ho^z$ 的一个零点在 $z=1$ 处夹紧实轴，从而产生一阶 Rényi 相变。
英文摘要
Extracting operationally meaningful quantities such as von Neumann entropy and mutual information is central to characterizing many-body quantum systems, yet experiments and numerics often provide direct access only to integer Rényi entropies. Whereas conventional extrapolation relies on a prescribed fitting ansatz, in PRL 137, 100202 we introduced an alternative approach based on stabilized analytic continuation (SAC), which avoids such an ansatz and is inherently robust to noise. Here, we further develop this framework in the noiseless setting and benchmark its performance across several nontrivial many-body problems. We first show that, besides the intrinsic ambiguity of reconstructing the von Neumann entropy from finitely many Rényi samples, analytic continuation can also fail because of genuine nonanalyticities in the Rényi function arising from zeros of $\text{Tr}ρ^z$. We derive universal zero-free domains for $\text{Tr}ρ^z$ and systematically sharpen these bounds using additional spectral information about $ρ$. We then benchmark the performance of SAC in three settings: ($i$) extracting topological entanglement entropy from DMRG Rényi data for the toric code and Kagome Heisenberg models; ($ii$) reconstructing the mutual information between disjoint intervals in a $(1+1)d$ compact-boson CFT; and ($iii$) recovering finite-time ballistic growth of the von Neumann entropy from integer Rényi entropies that cross over toward subballistic growth in diffusive quantum dynamics. In the latter setting, analytic continuation is expected to fail in the long time limit. We illustrate this mechanism with a physically motivated two-sector model, where the asymptotic separation between von Neumann and higher-Rényi growth is accompanied by a zero of $\text{Tr}ρ^z$ pinching the real axis at $z=1$, thereby producing a first-order Rényi phase transition.
Comments30 pages, 13 figures
