38 research outputs found
Self-Consistent Tensor Product Variational Approximation for 3D Classical Models
We propose a numerical variational method for three-dimensional (3D)
classical lattice models. We construct the variational state as a product of
local tensors, and improve it by use of the corner transfer matrix
renormalization group (CTMRG), which is a variant of the density matrix
renormalization group (DMRG) applied to 2D classical systems. Numerical
efficiency of this approximation is investigated through trial applications to
the 3D Ising model and the 3D 3-state Potts model.Comment: 12 pages, 6 figure
The Density Matrix Renormalization Group technique with periodic boundary conditions
The Density Matrix Renormalization Group (DMRG) method with periodic boundary
conditions is introduced for two dimensional classical spin models. It is shown
that this method is more suitable for derivation of the properties of infinite
2D systems than the DMRG with open boundary conditions despite the latter
describes much better strips of finite width. For calculation at criticality,
phenomenological renormalization at finite strips is used together with a
criterion for optimum strip width for a given order of approximation. For this
width the critical temperature of 2D Ising model is estimated with seven-digit
accuracy for not too large order of approximation. Similar precision is reached
for critical indices. These results exceed the accuracy of similar calculations
for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.
Magnetization process for a quasi-one-dimensional S=1 antiferromagnet
We investigate the magnetization process for a quasi-one-dimensional S=1
antiferromagnet with bond alternation. By combining the density matrix
renormalization group method with the interchain mean-field theory, we discuss
how the interchain coupling affects the magnetization curve. It is found that
the width of the magnetization plateau is considerably reduced upon introducing
the interchain coupling. We obtain the phase diagram in a magnetic field. The
effect of single-ion anisotropy is also addressed.Comment: 6 pages, 7 eps figure
Construction of a matrix product stationary state from solutions of finite size system
Stationary states of stochastic models, which have states per site, in
matrix product form are considered. First we give a necessary condition for the
existence of a finite -dimensional matrix product state for any .
Second, we give a method to construct the matrices from the stationary states
of small size system when the above condition and are satisfied.
Third, the method by which one can check that the obtained matrices are valid
for any system size is presented for the case where is satisfied. The
application of our methods is explained using three examples: the asymmetric
exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen.
36 (2003) 7497] and a hybrid of both of the models.Comment: 22 pages, no figure. Major changes: sec.3 was shortened; the list of
references were changed. This is the final version, which will appear in
J.Phys.
Efficiency of symmetric targeting for finite-T DMRG
Two targeting schemes have been known for the density matrix renormalization
group (DMRG) applied to non-Hermitian problems; one uses an asymmetric density
matrix and the other uses symmetric density matrix. We compare the numerical
efficiency of these two targeting schemes when they are used for the finite
temperature DMRG.Comment: 4 pages, 3 Postscript figures, REVTe
Magnetic-Field-Induced Antiferromagnetism in Two-Dimensional Hubbard Model: Analysis of CeRhIn
We propose the mechanism for the magnetic-field-induced antiferromagnetic
(AFM) state in a two-dimensional Hubbard model in the vicinity of the AFM
quantum critical point (QCP), using the fluctuation-exchange (FLEX)
approximation by taking the Zeeman energy due to the magnetic field into
account. In the vicinity of the QCP, we find that the AFM correlation
perpendicular to is enhanced, whereas that parallel to is reduced. This
fact means that the finite magnetic field increases , with the AFM order
perpendicular to . The increment in can be understood in terms of the
reduction of both quantum and thermal fluctuations due to the magnetic field,
which is caused by the self-energy effect within the FLEX approximation. The
present study naturally explains the increment in in CeRhIn_5 under the
magnetic field found recently.Comment: 5 page
Quasi-one-dimensional anisotropic Heisenberg model in a transverse magnetic field
The phase diagram of weakly coupled chains in a transverse magnetic
field is studied using the mean-field approximation for the interchain coupling
and known exact results for an effective one-dimensional model. Results are
applied to the quasi-one-dimensional antiferromagnet and the
value of interchain interaction in this compound is estimated.Comment: 4 pages, 2 figure
Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the
Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase
transition in the directed percolation universality class. Estimates for the
stochastic time evolution, phase boundaries and critical exponents can be
obtained with high precision. This is possible using only modest numerical
effort since the thermodynamic limit can be taken analytically in our approach.
We also point out further advantages of the TMRG over other numerical
approaches, such as classical DMRG or Monte-Carlo simulations.Comment: 9 pages, 9 figures, uses IOP styl
Gap generation in the XXZ model in a transverse magnetic field
The ground state phase diagram of the 1D XXZ model in transverse magnetic
field is obtained. It consists of the gapped phases with different types of
long range order (LRO) and critical lines at which the gap and the LRO vanish.
Using scaling estimations and a mean-field approach as well as numerical
results we found critical indices of the gap and the LRO in the vicinity of all
critical lines.Comment: 4 pages, 1 figure, Late
Quantum Phase Transitions in the One-Dimensional S=1 Spin-Orbital Model: Implications for Cubic Vanadates
We investigate ground-state properties and quantum phase transitions in the
one-dimensional S=1 spin-orbital model relevant to cubic vanadates. Using the
density matrix renormalization group, we compute the ground-state energy, the
magnetization and the correlation functions for different values of the Hund's
coupling and the external magnetic field. It is found that the
magnetization jumps at a certain critical field, which is a hallmark of the
field-induced first-order phase transition. The phase transition driven by
is also of first order. We also consider how the lattice-induced
ferro-type interaction between orbitals modifies the phase diagram, and discuss
the results in a context of the first-order phase transition observed in
YVO at 77K.Comment: 7 pages, 7 figur