标题： 二维量子系统的全局张量网络重正化：从热转变中探测普遍数据的新窗口 显示英文标题

标题： Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions

摘要： 我们提出了一种基于全局优化的新张量网络重正化群（TNR）方案，并引入了一种构建二维量子系统有限温度密度矩阵的新方法。 将这两者结合，形成一种称为热张量网络重正化（TTNR）的新算法，我们在热力学相变点获得了高度精确的共形场论（CFT）数据。 这为数值识别相变提供了一条新的高效途径，为传统的通过临界指数分析提供了替代方案。 显示英文摘要

摘要： We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a new algorithm called thermal tensor network renormalization (TTNR), we obtain highly accurate conformal field theory (CFT) data at thermal transition points. This provides a new and efficient route for numerically identifying phase transitions, offering an alternative to the conventional analysis via critical exponents.