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

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.