Quantum entanglement for tensor product states and numerical renormalization groups

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Recently, the numerical renormalization group based on the tensor product state plays a fundamental role in analyzing the ground state of the quantum many body system.We firstly clalified that the key mechanizm of the Wilon-type renromalization group is in the scale free property of the energy scale. We next found out that the fixed point structure of the higher order tensor renormalization group can be explained by doubling of the corner transfer matrix in the off critical region. We also clarified that this result is basically universal for both of the one-dimensional quantum system and two dimensional classical systems.