Extension of DMRG by explicit construction of Density Matrices

点击翻译按钮获取中文摘要

In the finite temperature density matrix renormalization group (DMRG) they normally construct the density matrices by cutting a cylinder which correspond ; to the finite temperature one-dimensional (ID) quantum systems. In this case, the topology of the 2D system (= cylinder) is different from the plane, conventional and simple construction of the density matrix is not always most efficient in the sense of free-energy minimum. This is because there is information exchange around the cylinder, which is not properly included by the conventional method. There is similar difficulty in DMRG for 3D classical systems.We thus return back to the principle of DMRG, we consider an efficient construction of the density matrix from the view point of the variational states represented as tensor product and their improvements. As a result, we obtained an equation that optimizes the tensor product state. In addition, we find that the equation can be solved numerically by way of the corner transfer renormalization group method (CTMRG).We apply the new variational method thus obtained, the tensor product variational approxi-mation (TPVA) to 3D Ising and Potts models, and obtained the transition temperatures and latent heats, that are comparable to those obtained by Monte Carlo simulations.We also drawed the phase diagram of the 16-vertex model by applying CTMRG method to the 16-vertex model, in the parameter region that is not investigated so far.