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

Atsushi Ueda; Sander De Meyer; Adwait Naravane; Victor Vanthilt; Frank Verstraete

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arXiv · 2508.05406

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

Atsushi Ueda·Sander De Meyer·Adwait Naravane·Victor Vanthilt·Frank Verstraete

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Abstract

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.

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Atsushi Ueda, Sander De Meyer, Adwait Naravane, Victor Vanthilt, Frank Verstraete. 2025-08-07. Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions. https://arxiv.org/abs/2508.05406

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