Fixed Point of the Finite System DMRG
Hiroshi Takasaki, Toshiya Hikihara, Tomotoshi Nishino · Journal of the Physical Society of Japan · 1999
The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B••B. This is because the tensors are not improved directly. We overcome this problem by using the simpler block structure B • B for the final several sweeps in the finite iteration process. It is possible to increase the numerical precision of the finite system algorithm without increasing the computational effort. Establishment of the density matrix renormalization group (DMRG) by White [1] is one of the major progresses in computational condensed matter physics. DMRG enables us to calculate ground states of relatively large scale one-dimensional (1D) quantum systems. [2, 3, 4, 5, 6]. Two-dimensional (2D) classical systems, [7, 8, 9, 10] and 1D quantum system at finite temperature [11, 12, 13, 14] have also been investigated. Östlund and Rommer [15] examined the thermodynamic limit (N → ∞) of the infinite system algorithm, and they pointed out that the block state B corresponds to a product of position independent tensor. It should be noted that their result does not show that