Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) ${O(2)\times O(2)}$ symmetries, which is broken to ${O(2)}$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem ${A}$ with length ${L_A}$ corresponds to the energy of the half-vortex pair ${S\sim \rho_s \log L_A}$, where ${\rho_s}$ is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.

中文翻译：

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非厄米 SYK$_2$ 链中的紧急副本保形对称

最近，发现非幺正自由费米子动力学的稳态表现出具有幂律平方相关性和对数子系统纠缠的新临界相位。在这项工作中，我们通过构建具有非厄米动力学的可解静态/布朗二次 Sachdev-Ye-Kitaev 链，从理论上理解了基础物理学。我们发现复制系统的动作通常显示（一个或无限个副本）${O(2)\times O(2)}$ 对称性，它被鞍点分解为 ${O(2)}$解决方案。这导致了戈德斯通模式的紧急共形场理论。我们推导出有效动作并获得平方相关器的普遍临界行为。此外，长度为 ${L_A}$ 的子系统 ${A}$ 的纠缠熵对应于半涡旋对 ${S\sim \rho_s \log L_A}$ 的能量，其中 ${\rho_s}$ 是Goldstone 模式的总刚度。我们还讨论了不止一个 Goldstone 模式分支的特殊限制，并评论了交互效果。