Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0101360,
title = {Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz},
author = {Nobuya Maeshima and Yasuhiro Hieida and Yasuhiro Akutsu and Tomotoshi Nishino and Kouichi Okunishi},
journal= {arXiv preprint arXiv:cond-mat/0101360},
year = {2008}
}
Comments
Unnecessary files are removed. 8 pages, 7 figures, submitted to Phys.Rev.E