Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-01-23
Phys.Rev.E64:016705,2001
Physics
Condensed Matter
Statistical Mechanics
Unnecessary files are removed. 8 pages, 7 figures, submitted to Phys.Rev.E
Scientific paper
10.1103/PhysRevE.64.016705
We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors which are iteratively optimized by the use of the ``vertical density matrix'' formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation, we can also apply the VDMA to two-dimensional (2D) quantum systems, which we demonstrate for the 2D transverse field Ising model.
Akutsu Yasuhiro
Hieida Yasuhiro
Maeshima Nobuya
Nishino Tomotoshi
Okunishi Kouichi
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