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 are 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.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 are 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.

arXiv:cond-mat/9706124Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsOct 1, 199719 citations

Density matrix renormalization group

Haibo Ma, Ulrich Schollwöck, Zhigang Shuai

Elsevier eBooksJan 1, 20223 citations

Phase Diagram of a 2D Vertex Model

Hiroshi Takasaki, Tomotoshi Nishino, Yasuhiro Hieida

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $β= 1/8$ and $α= 0$ .Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $β= 1/8$ and $α= 0$.

arXiv:cond-mat/0012490Journal of the Physical Society of JapanMay 15, 200110 citations

The Density Matrix Renormalization Group

R. M. Noack, Steven R. White

Springer eBooksApr 6, 200822 citations

22 Dynamical Density-Matrix Renormalization Group

Eric Jeckelmann, H. Benthien

Jan 1, 20080 citations

K=1.0866

and obtain

c=1.006(1)

for the conformal anomaly.

β= 1/8

and

α= 0