585 research outputs found
Exact ground states of quantum spin-2 models on the hexagonal lattice
We construct exact non-trivial ground states of spin-2 quantum
antiferromagnets on the hexagonal lattice. Using the optimum ground state
approach we determine the ground state in different subspaces of a general
spin-2 Hamiltonian consistent with some realistic symmetries. These states,
which are not of simple product form, depend on two free parameters and can be
shown to be only weakly degenerate. We find ground states with different types
of magnetic order, i.e. a weak antiferromagnet with finite sublattice
magnetization and a weak ferromagnet with ferrimagnetic order. For the latter
it is argued that a quantum phase transition occurs within the solvable
subspace.Comment: 7 pages, accepted for publication in Phys. Rev.
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Phase diagram of the asymmetric tetrahedral Ising-Heisenberg chain
The asymmetric tetrahedron is composed by all edges of tetrahedron
represented by Ising interaction except one, which has a Heisenberg type
interaction. This asymmetric tetrahedron is arranged connecting a vertex which
edges are only Ising type interaction to another vertex with same structure of
another tetrahedron. The process is replicated and this kind of lattice we call
the asymmetric Ising-Heisenberg chain. We have studied the ground state phase
diagram for this kind of models. Particularly we consider two situations in the
Heisenberg-type interaction, (i) The asymmetric tetrahedral spin(1/2,1/2)
Ising-XYZ chain, and (ii) the asymmetric tetrahedral spin-(1/2,1) Ising-XXZ
chain, where we have found a rich phase diagram and a number of multicritical
points. Additionally we have also studied their thermodynamics properties and
the correlation function, using the decorated transformation. We have mapped
the asymmetric tetrahedral Ising-Heisenberg chain in an effective Ising chain,
and we have also concluded that it is possible to evaluate the partition
function including a longitudinal external magnetic field.Comment: 14 pages, 8 figures. Accepted in Journal of Physics: Condensed Matte
Stripe Ansatzs from Exactly Solved Models
Using the Boltzmann weights of classical Statistical Mechanics vertex models
we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems,
characterized by a strong anisotropy, which gives rise to stripe like
structures. In the case of the six vertex model we compute exactly, in the
thermodynamic limit, the norm of the ansatz and other observables. Employing
this ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ
Hamiltonians along the legs coupled by an Ising term. Finally, we suggest a
connection between the six and eight-vertex Anisotropic Tensor Product Ansatzs,
and their associated Hamiltonians, with the smectic stripe phases recently
discussed in the literature.Comment: REVTEX4.b4 file, 10 pages, 2 ps Figures. Revised version to appear in
PR
A Density Matrix Algorithm for 3D Classical Models
We generalize the corner transfer matrix renormalization group, which
consists of White's density matrix algorithm and Baxter's method of the corner
transfer matrix, to three dimensional (3D) classical models. The
renormalization group transformation is obtained through the diagonalization of
density matrices for a cubic cluster. A trial application for 3D Ising model
with m=2 is shown as the simplest case.Comment: 15 pages, Latex(JPSJ style files are included), 8 ps figures,
submitted to J. Phys. Soc. Jpn., some references are correcte
Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
The stationary state of a stochastic process on a ring can be expressed using
traces of monomials of an associative algebra defined by quadratic relations.
If one considers only exclusion processes one can restrict the type of algebras
and obtain recurrence relations for the traces. This is possible only if the
rates satisfy certain compatibility conditions. These conditions are derived
and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.
Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
We show in the example of a one-dimensional asymmetric exclusion process that
stationary states of models with parallel dynamics may be written in a matrix
product form. The corresponding algebra is quadratic and involves three
different matrices. Using this formalism we prove previous conjectures for the
equal-time correlation functions of the model.Comment: LaTeX, 8 pages, one postscript figur
Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
We discuss zero-temperature quantum spin chains in a uniform magnetic field,
with axial symmetry. For integer or half-integer spin, , the magnetization
curve can have plateaus and we argue that the magnetization per site is
topologically quantized as at the plateaus, where is
the period of the groundstate. We also discuss conditions for the presence of
the plateau at those quantized values. For and , we study
several models and find two distinct types of massive phases at the plateau.
One of them is argued to be a ``Haldane gap phase'' for half-integer .Comment: Revised version, to appear in Phys. Rev. Lett. (no changes in main
conclusions); 5 pages, REVTEX with 2 figures in ep
Mixed-spin systems: coexistence of Haldane gap and antiferromagnetic long range order
Recent experiments on the quasi-1D antiferromagnets (R =
rare earth) have shown the existence of purely 1D Haldane gap excitations
propagating on the Ni chains. Below an ordering temperature, the gap
excitations survive and coexist with the conventional spin waves in the ordered
phase. We construct a model mixed-spin system in 2D for which the ground state
can be exactly specified. Using the Matrix Product Method, we show the
existence of Haldane gap excitations in the ordered phase. We consider
different cases of ordering to study the effect of ordering on the degeneracy
of the Haldane gap excitations.Comment: 13 pages, LaTeX, 2 Postscript figures, communicated to Phys. Rev.
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