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 optimizatio...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.展开更多
基金supported by the National R&D Program of China (Grant No. 2017YFA0302900)the National Natural Science Foundation of China (Grant Nos. 11774420 and 12134020)+1 种基金the Natural Science Foundation of Hunan Province (Grant No. 851204035)the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant No. 20XNLG19)
文摘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.
