arXiv 2606.193312026-06cond-mat.stat-mechhep-thnlin.CDquant-ph

拓扑谱形状因子揭示来自多体量子混沌的涌现非厄米单粒子$\mathcal{PT}$相变

Topological spectral form factor reveals emergent non-Hermitian single-particle $\mathcal{PT}$ transitions from many-body quantum chaos

Lancaster University（兰卡斯特大学）；University of Warwick（华威大学）；Northumbria University（诺森比亚大学）

Daniel Harkin, Chun Y. Leung, Amos Chan

备注：: 10+74 pages, 5+41 figures

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AI总结：

通过插入拓扑缺陷定义拓扑谱形状因子，将其映射到(3+1)D非厄米单粒子问题，发现有效时间畴壁动力学在有限相互作用强度下发生$\mathcal{PT}$对称性破缺相变。

摘要：

在平衡态物理中，量子与经典配分函数中的拓扑缺陷插入提供了超越局域观测量的相变非微扰探针。在非平衡物理中，谱形状因子提供了普适量子动力学的最小探针，并可表示为两个虚逆温度配分函数的乘积。我们通过在加倍配分函数上非平凡作用的拓扑缺陷插入来定义拓扑谱形状因子（TopSFF），产生不匹配的时空世界面拓扑。对于由全局交换算符实现的最小$\mathbb{Z}_2$空间扩展缺陷，我们推导出通用一维多体混沌系统的TopSFF到描述时间畴壁（tDW）的涌现$(3+1)$D非厄米单粒子问题的精确映射。我们解析证明，有效tDW动力学在有限相互作用强度$\epsilon_{\mathrm{EP}}$处经历$\mathcal{PT}$对称性破缺相变：低于$\epsilon_{\mathrm{EP}}$时，主导模式极化到高斯或非高斯tDW扇区，TopSFF随系统尺寸单调指数变化；高于$\epsilon_{\mathrm{EP}}$时，tDW扇区混合，TopSFF随系统尺寸振荡；在异常点$\epsilon_{\mathrm{EP}}$处，Jordan非对角性产生线性于系统尺寸的增强。对于时间扩展拓扑缺陷，我们推导出具有时间反演或时间平移对称性系统中TopSFF自由能的精确普适标度形式，并在独立模型中通过数值验证。

英文摘要：

In equilibrium, topological defect insertions in quantum and classical partition functions provide non-perturbative probes of phase transitions beyond local observables. In non-equilibrium physics, the spectral form factor provides a minimal probe of universal quantum dynamics and is a product of two partition functions at imaginary inverse temperature. We define the topological spectral form factor (TopSFF) by inserting topological defects acting non-trivially on the doubled partition functions, producing mismatched spacetime world-sheet topologies. For the minimal $\mathbb{Z}_2$ spatially extended defect, implemented by the global swap operator, we derive an exact mapping of the TopSFF of a generic $(1+1)$D many-body chaotic system to an emergent $(3+1)$D non-Hermitian single-particle problem describing a temporal domain wall (tDW). We show analytically that the effective tDW dynamics undergoes a $\mathcal{PT}$ symmetry breaking transition at finite interaction strength $ε_{\mathrm{EP}}$: below $ε_{\mathrm{EP}}$, the leading modes are polarized into Gaussian or non-Gaussian tDW sectors and the TopSFF varies monotonically and exponentially with system size; above $ε_{\mathrm{EP}}$, the tDW sectors hybridize and the TopSFF oscillates with system size; at the exceptional point $ε_{\mathrm{EP}}$, Jordan non-diagonality produces a linear-in-system-size enhancement. For minimal temporally extended topological defects associated with global swap or time translation, we derive exact universal TopSFF free-energy scaling forms. We verify these signatures numerically in independent models.

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