Abstract：In the context of tensor network states, we for the first time reformulate the corner transfer matrix renormalization group (CTMRG) method into a variational bilevel optimization algorithm. The solution of the optimization problem corresponds to the fixed-point environment pursued in the conventional CTMRG method, from which the partition function of a classical statistical model, represented by an infinite tensor network, can be efficiently evaluated. The validity of this variational idea is demonstrated by the high-precision calculation of the residual entropy of the dimer model, and is further verified by investigating several typical phase transitions in classical spin models, where the obtained critical points and critical exponents all agree with the best known results in literature. Its extension to three-dimensional tensor networks or quantum lattice models is straightforward, as also discussed briefly.
. [J]. 中国物理快报, 2022, 39(6): 67502-067502.
X. F. Liu, Y. F. Fu, W. Q. Yu, J. F. Yu, and Z. Y. Xie. Variational Corner Transfer Matrix Renormalization Group Method for Classical Statistical Models. Chin. Phys. Lett., 2022, 39(6): 67502-067502.
LeBlanc J P F, Antipov A E, Becca F, Bulik I W, Chan G K L, Chung C M, Deng Y, Ferrero M, Henderson T M, Jiménez-Hoyos C A, Kozik E, Liu X W, Millis A J, Prokof'ev N V, Qin M, Scuseria G E, Shi H, Svistunov B V, Tocchio L F, Tupitsyn I S, White S R, Zhang S, Zheng B X, Zhu Z, and Gull E (Simons Collaboration on the Many-Electron Problem) 2015 Phys. Rev. X5 041041
Ran S J, Tirrito E, Peng C, Chen X, Tagliacozzo L, Su G, and Lewenstein M 2020 Tensor Network Contractions: Methods and Applications to Quantum Many-Body Systems (Springer Nature)
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