受监测的 Brownian SYK 簇的场论
Field theory for monitored Brownian SYK clusters
AI总结：
本文研究受监测的 Brownian SYK 簇的演化，通过推广自旋相干态构建路径积分，导出描述量子涨落的有效场论，并揭示稳态下双簇纠缠与 N 成正比。
摘要：
我们考虑多个 Brownian Sachdev-Ye-Kitaev (SYK) 簇的时间演化，即包含 N 个 Majorana 费米子并带有噪声相互作用项的系统。除了幺正演化外，我们引入了双费米子监测。我们通过将自旋相干态推广至更高对称群，构建了该动力学的相干态路径积分。随后我们证明，复制的密度矩阵的演化可以由“轻”自由度的有效场论来描述，即由幺正演化产生的量子涨落。该方法被应用于二次型情形（此时场论退化为非线性 sigma 模型 (NLSM)）以及相互作用的 SYK 簇。我们展示了在稳态区域，两个受监测的簇表现出与 N 成正比的纠缠，其比例因子取决于幺正耦合的强度。
英文摘要：
We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev (SYK), i.e. systems of N Majorana fermions with a noisy interaction term. In addition to the unitary evolution, we introduce two-fermion monitorings. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. We then demonstrate that the evolution of the replicated density matrix can be described by an effective field theory for the "light" degrees of freedom, i.e. the quantum fluctuations generated by the unitary evolution. This method is applied to both quadratic, where the field theory reduces to the nonlinear sigma model (NLSM), and also to interacting SYK clusters. We show that in the stationary regime, two monitored clusters exhibit linear-in-N entanglement, with a proportionality factor dependent on the strength of the unitary coupling.
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