标题： 远离平衡的费米子量子临界性 显示英文标题

标题： Fermion quantum criticality far from equilibrium

摘要： 将量子系统从平衡状态驱动到非平衡状态，同时在大尺度上保持其微妙的量子力学关联，这是一个重大的挑战，无论是在基础层面还是技术应用方面。 从根本上说，这一挑战是通过如何让量子效应在渐近尺度上持续存在这个问题来明确的，这类似于平衡态中的量子临界点。 在这项工作中，我们使用费米子作为构建模块来构造这样的情景。 这些费米子在两个拓扑不同且具有量子关联的暗态之间经历吸收态到吸收态的相变。 从一个微观的、相互作用的Lindbladian出发，我们推导出一个有效的Lindblad-Keldysh场论，在这个理论中，临界费米子与一个玻色子浴耦合，该浴具有与粒子数守恒相关的流体动力学涨落。 这个场论的一个关键特征是出现的对称性，它在热浴存在的情况下保护费米子状态的纯度。 我们通过围绕上临界维度的领先阶展开来定量表征临界点，从而建立了第一个非平衡费米子普适类。 这种对称性保护机制表现出与定向渗流问题的相似之处，这表明了在费米子系统中通往更广泛的一类鲁棒、普适量子现象的路径。 显示英文摘要

摘要： Driving a quantum system out of equilibrium while preserving its subtle quantum mechanical correlations on large scales presents a major challenge, both fundamentally and for technological applications. At its core, this challenge is pinpointed by the question of how quantum effects can persist at asymptotic scales, analogous to quantum critical points in equilibrium. In this work, we construct such a scenario using fermions as building blocks. These fermions undergo an absorbing-to-absorbing state transition between two topologically distinct and quantum-correlated dark states. Starting from a microscopic, interacting Lindbladian, we derive an effective Lindblad-Keldysh field theory in which critical fermions couple to a bosonic bath with hydrodynamic fluctuations associated with particle number conservation. A key feature of this field theory is an emergent symmetry that protects the purity of the fermions' state even in the presence of the thermal bath. We quantitatively characterise the critical point using a leading-order expansion around the upper critical dimension, thereby establishing the first non-equilibrium universality class of fermions. The symmetry protection mechanism, which exhibits parallels to the problem of directed percolation, suggests a pathway toward a broader class of robust, universal quantum phenomena in fermionic systems.