受监测超导链中的超对数纠缠标度
Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain
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中文总结 AI 辅助
研究受监测的一维自旋ful s波BCS链在罕见测量 regime下的纠缠动力学，通过开发Keldysh- replica NLSM，经分析发现测量反作用等施加质量约束，产生弱反局域化流，实现超对数稳态纠缠标度S(L)∼ln²L，解释了相关数值证据。
中文摘要 AI 辅助
我们为受监测的一维自旋ful s波BCS链在罕见测量 regime（γ≪J，Δ）下的纠缠动力学开发了一个Keldysh- replica非线性西格玛模型（NLSM）。尽管干净的自旋ful s波BCS哈密顿量属于对称类CI，但自旋分辨测量和投影到守恒f扇区将有效问题简化为C类。从相应的父辛鞍点出发，我们表明测量反作用和配对振幅施加了互补的质量约束，使不同的波动通道有能隙。它们的相互作用将存活的无质量模式动态投影到 replica空间中的SO(R)目标流形上。对该SO(R) NLSM的单圈重整化群分析表明，在 replica极限R→1时，β函数变为负，产生弱反局域化流。这种流在罕见测量 regime中产生超对数稳态纠缠标度S(L)∼ln²L。我们的场论结果解释了配套论文中报道的数值证据，并表明拓扑平凡的受监测s波超导体可以在不依赖Wess-Zumino-Witten项的情况下实现SO(R)弱反局域化临界相。
英文摘要
We study the entanglement dynamics of a one-dimensional spinful $s$-wave superconductor subjected to local continuous measurements. In the rare-measurement regime, we derive a replicated Keldysh non-linear sigma model (NLSM) to describe the steady-state entanglement. Within this field-theoretic framework, the interplay between measurement dephasing and superconducting pairing constrains the low-energy, long-wavelength fluctuations to an $\mathrm{SO(R)}$ target manifold. A one-loop renormalization-group analysis shows that the theory develops a weak-anti-localization flow, stabilizing a critical phase with super-logarithmic scaling of the steady-state entanglement. Our field-theoretic results explain the numerical evidence reported in the companion Letter [arXiv:2604.04375] and demonstrate that such a critical phase can emerge in a one-dimensional topologically trivial superconductor without relying on topological protection.
