Chin. Phys. Lett.  2022, Vol. 39 Issue (6): 067502    DOI: 10.1088/0256-307X/39/6/067502
Variational Corner Transfer Matrix Renormalization Group Method for Classical Statistical Models
X. F. Liu1†, Y. F. Fu1†, W. Q. Yu1, J. F. Yu2*, and Z. Y. Xie1*
1Department of Physics, Renmin University of China, Beijing 100872, China
2School of Physics and Electronics, Hunan University, Changsha 410082, China
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X. F. Liu, Y. F. Fu, W. Q. Yu et al  2022 Chin. Phys. Lett. 39 067502
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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.
Received: 31 March 2022      Express Letter Published: 11 May 2022
PACS:  05.10.Cc (Renormalization group methods)  
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X. F. Liu
Y. F. Fu
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J. F. Yu
and Z. Y. Xie
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