量子临界性中的关联与因果
Correlation versus Causation in Quantum Criticality
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中文总结 AI 辅助
该研究对比量子临界性中的关联与因果，揭示时间导数场不贡献静态响应的机制，用DMRG识别临界伊辛模型的初级算符，还解释边模局域化并构造极小分裂自旋链。
中文摘要 AI 辅助
关联函数⟨O₁(x)O₂(0)⟩通过空间衰减揭示标度维度，我们转而考虑静态磁化率，即通过O₂(0)微扰哈密顿量时⟨O₁(x)⟩的变化，简称因果。在共形场论（CFT）中，量纲分析预测关联的衰减为|x|^(-2Δ)，因果的衰减为|x|^(-2Δ+1)。然而我们发现，因果可通过一种通用机制在x方向多衰减15个数量级，该机制源于时间导数场无法对静态响应做贡献。在高维CFT中，该机制确保即使后代主导关联，因果的主导项仍来自初级算符；我们结合密度矩阵重整化群（DMRG），在(2+1)维临界伊辛模型中识别出此前未解决的角初级算符（Δ≈8.8）和重磁线缺陷初级算符（Δ≈4.6）。此外，相同机制支配(1+1)维无隙对称性保护拓扑相中的边模局域化，解释了此前观测到的异常小边模分裂，并指导我们构造出分裂小至1/L¹⁸和1/L²⁵的自旋链。
英文摘要
Correlation functions $\langle O_1(x) O_2(0) \rangle$ reveal scaling dimensions through spatial decay. We instead consider static susceptibility, the change in $\langle O_1(x) \rangle$ from perturbing the Hamiltonian by $O_2(0)$, which we term causation for short. In a conformal field theory (CFT), dimensional analysis predicts decay of $|x|^{-2Δ}$ for correlation and $|x|^{-2Δ+1}$ for causation. Yet we find causation can decay up to fifteen additional orders in $x$ through a general mechanism, which we trace to time-derivative fields being unable to contribute to static response. In higher-dimensional CFTs, this mechanism ensures leading causation arises from primaries, even when descendants dominate correlation, which we leverage with DMRG to identify a previously unresolved corner primary of $Δ\approx 8.8$ and a heavy magnetic line defect primary of $Δ\approx 4.6$ in the $(2+1)$D critical Ising model. Moreover, the same mechanism governs edge-mode localization in $(1+1)$D gapless symmetry-protected topological phases, explaining previously observed anomalously small edge-mode splittings and guiding our construction of spin chains with splittings as small as $1/L^{18}$ and $1/L^{25}$.
