张量网络的Uhlmann性质
Uhlmann fidelities from tensor networks
摘要：
给定量子多体系统的两个状态$|ψ\rangle$和$|ϕ\rangle$，可以使用重叠或保真度$|\langleψ|ϕ\rangle|$来量化它们的相似程度。为了进一步解决$|ψ\rangle$和$|ϕ\rangle$在空间上的相似性，可以考虑它们在系统的各个区域上的约化密度矩阵$ρ$和$σ$，并且计算Uhlmann保真度$F(ρ, σ) = \operatorname{Tr} \sqrt{\sqrtρ σ\sqrtρ}$。在本文中，我们将展示如何计算这样的子系统的quantiities可以有效地在许多情况下，当两个状态表示为张量网络。使用Uhlmann定理公式化，这样的子系统性能表现为矩阵乘积状态和树张量网络的某些子系统的自然量，并且评估它们在算法上是简单的并且计算上是负担得起的。我们证明了评估子系统的实用性与三个例子的应用：研究局部淬火，比较临界和非临界状态，并在张量网络模拟量化收敛。
英文摘要：
Given two states $|ψ\rangle$ and $|ϕ\rangle$ of a quantum many-body system, one may use the overlap or fidelity $|\langleψ|ϕ\rangle|$ to quantify how similar they are. To further resolve the similarity of $|ψ\rangle$ and $|ϕ\rangle$ in space, one can consider their reduced density matrices $ρ$ and $σ$ on various regions of the system, and compute the Uhlmann fidelity $F(ρ, σ) = \operatorname{Tr} \sqrt{\sqrtρ σ\sqrtρ}$. In this paper, we show how computing such subsystem fidelities can be done efficiently in many cases when the two states are represented as tensor networks. Formulated using Uhlmann's theorem, such subsystem fidelities appear as natural quantities to extract for certain subsystems for Matrix Product States and Tree Tensor Networks, and evaluating them is algorithmically simple and computationally affordable. We demonstrate the usefulness of evaluating subsystem fidelities with three example applications: studying local quenches, comparing critical and non-critical states, and quantifying convergence in tensor network simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
