Density-matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

摘要

We embody the density-matrix renormalization-group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model an classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed in reducing enormously the dimension of the matrix that has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction K = 1.0866 and obtain c = 1.006(1) for the conformal anomaly.