论文标题
多体统一动力学中可溶解的非铁皮皮肤效应
Solvable non-Hermitian skin effect in many-body unitary dynamics
论文作者
论文摘要
我们研究具有最近邻居随机门的电路中的两分纠缠的单一演变。在Qudits上的纯度动力学的紧凑型非单身描述中，我们发现纯度弛豫率突然过渡，其起源是在基础边界定位的特征模型中 - 皮肤效应。我们提供了问题的完整解决方案，是两个站点矩阵中最简单的迭代之一，即，每个矩阵仅是两个投影仪的总和。这导致了由核的约旦正常形式影响丰富的动力学，最重要的是，在热力学极限中完全不连续的频谱。它提供了一个简单的例子，说明了看似无害的多体统一进化如何具有有趣的数学效果：有效的非对称性toeplitz传递矩阵矩阵描述会导致幻影放松，因此矩阵谱系未给出正确的放松率，而是通过其pseudospectrum给出。
We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact non-unitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes -- the skin effect. We provide the full solution of the problem, being one of the simplest iterations of two-site matrices, namely, that each is a sum of only two projectors. This leads to rich dynamics influenced by the Jordan normal form of the kernel and, most importantly, a spectrum that is completely discontinuous in the thermodynamic limit. It provides a simple example of how a seemingly innocuous many-body unitary evolution can harbor interesting mathematical effects: an effective non-symmetric Toeplitz transfer matrix description causes a phantom relaxation, such that the correct relaxation rate is not given by the matrix spectrum, but rather by its pseudospectrum.
