Tensor renormalization group algorithms with a projective truncation method
Y Nakamura, H Oba, S Takeda - Physical Review B, 2019 - APS
Y Nakamura, H Oba, S Takeda
Physical Review B, 2019•APSWe apply the projective truncation technique to the tensor renormalization group (TRG)
algorithm in order to reduce the computational cost from O (χ 6) to O (χ 5), where χ is the
bond dimension, and propose three kinds of algorithms for demonstration. On the other
hand, the technique causes a systematic error due to the incompleteness of a projector
composed of isometries and in addition requires iteration steps to determine the isometries.
Nevertheless, we find that the accuracy of the free energy for the Ising model on a square …
algorithm in order to reduce the computational cost from O (χ 6) to O (χ 5), where χ is the
bond dimension, and propose three kinds of algorithms for demonstration. On the other
hand, the technique causes a systematic error due to the incompleteness of a projector
composed of isometries and in addition requires iteration steps to determine the isometries.
Nevertheless, we find that the accuracy of the free energy for the Ising model on a square …
We apply the projective truncation technique to the tensor renormalization group (TRG) algorithm in order to reduce the computational cost from to , where is the bond dimension, and propose three kinds of algorithms for demonstration. On the other hand, the technique causes a systematic error due to the incompleteness of a projector composed of isometries and in addition requires iteration steps to determine the isometries. Nevertheless, we find that the accuracy of the free energy for the Ising model on a square lattice is recovered to the level of TRG with a few iteration steps even at the critical temperature for , 48, and 64.