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

Monte Carlo renormalization group study of first order phase transitions

Anna Hazenfratz

Nuclear Physics B - Proceedings SupplementsSep 1, 19872 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

Renormalization - group properties of some vertex models

Carlos S. O. Yokoi, Silvio R. A. Salinas

Brazilian Journal of PhysicsJan 1, 19930 citations

Quantum phases and phase transitions of frustrated hard-core bosons on a triangular ladder

Tapan Mishra, Ramesh V. Pai, Subroto Mukerjee +1 more

Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.

arXiv:1210.7323Physical Review BMay 9, 201335 citations

K=1.0866

and obtain

c=1.006(1)

for the conformal anomaly.

β= 1/8

and

α= 0