7,529 research outputs found
Exactly solvable interacting vertex models
We introduce and solvev a special family of integrable interacting vertex
models that generalizes the well known six-vertex model. In addition to the
usual nearest-neighbor interactions among the vertices, there exist extra
hard-core interactions among pair of vertices at larger distances.The
associated row-to-row transfer matrices are diagonalized by using the recently
introduced matrix product {\it ansatz}. Similarly as the relation of the
six-vertex model with the XXZ quantum chain, the row-to-row transfer matrices
of these new models are also the generating functions of an infinite set of
commuting conserved charges. Among these charges we identify the integrable
generalization of the XXZ chain that contains hard-core exclusion interactions
among the spins. These quantum chains already appeared in the literature. The
present paper explains their integrability.Comment: 20 pages, 3 figure
Exactly Solvable Interacting Spin-Ice Vertex Model
A special family of solvable five-vertex model is introduced on a square
lattice. In addition to the usual nearest neighbor interactions, the vertices
defining the model also interact alongone of the diagonals of the lattice. Such
family of models includes in a special limit the standard six-vertex model. The
exact solution of these models gives the first application of the matrix
product ansatz introduced recently and applied successfully in the solution of
quantum chains. The phase diagram and the free energy of the models are
calculated in the thermodynamic limit. The models exhibit massless phases and
our analyticaland numerical analysis indicate that such phases are governed by
a conformal field theory with central charge and continuosly varying
critical exponents.Comment: 14 pages, 11 figure
Critical Behaviour of Mixed Heisenberg Chains
The critical behaviour of anisotropic Heisenberg models with two kinds of
antiferromagnetically exchange-coupled centers are studied numerically by using
finite-size calculations and conformal invariance. These models exhibit the
interesting property of ferrimagnetism instead of antiferromagnetism. Most of
our results are centered in the mixed Heisenberg chain where we have at even
(odd) sites a spin-S (S') SU(2) operator interacting with a XXZ like
interaction (anisotropy ). Our results indicate universal properties
for all these chains. The whole phase, , where the models change
from ferromagnetic to ferrimagnetic behaviour is
critical. Along this phase the critical fluctuations are ruled by a c=1
conformal field theory of Gaussian type. The conformal dimensions and critical
exponents, along this phase, are calculated by studying these models with
several boundary conditions.Comment: 21 pages, standard LaTex, to appear in J.Phys.A:Math.Ge
Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size
A generalization of the simple exclusion asymmetric model is introduced. In
this model an arbitrary mixture of molecules with distinct sizes , in units of lattice space, diffuses asymmetrically on the lattice.
A related surface growth model is also presented. Variations of the
distribution of molecules's sizes may change the excluded volume almost
continuously. We solve the model exactly through the Bethe ansatz and the
dynamical critical exponent is calculated from the finite-size corrections
of the mass gap of the related quantum chain. Our results show that for an
arbitrary distribution of molecules the dynamical critical behavior is on the
Kardar-Parizi-Zhang (KPZ) universality.Comment: 28 pages, 2 figures. To appear in Phys. Rev. E (1999
The Wave Functions for the Free-Fermion Part of the Spectrum of the Quantum Spin Models
We conjecture that the free-fermion part of the eigenspectrum observed
recently for the Perk-Schultz spin chain Hamiltonian in a finite
lattice with is a consequence of the existence of a
special simple eigenvalue for the transfer matrix of the auxiliary
inhomogeneous vertex model which appears in the nested Bethe ansatz
approach. We prove that this conjecture is valid for the case of the SU(3) spin
chain with periodic boundary condition. In this case we obtain a formula for
the components of the eigenvector of the auxiliary inhomogeneous 6-vertex model
(), which permit us to find one by one all components of
this eigenvector and consequently to find the eigenvectors of the free-fermion
part of the eigenspectrum of the SU(3) spin chain. Similarly as in the known
case of the case at our numerical and analytical
studies induce some conjectures for special rates of correlation functions.Comment: 25 pages and no figure
The phase diagram of the anisotropic Spin-1 Heisenberg Chain
We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum
chain. In studing this model we aim to clarify controversials about the point
where the massive Haldane phase appears.Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencode
The Finite Size SU(3) Perk-Schultz Model with Deformation Parameter q=exp(i 2 pi/3)
From extensive numeric diagonalizations of the SU(3) Perk-Schultz Hamiltonian
with a special value of the anisotropy and different boundary conditions, we
have observed simple regularities for a significant part of its eigenspectrum.
In particular the ground state energy and nearby excitations belong to this
part of the spectrum.
Our simple formulae describing these regularities remind, apart from some
selection rules, the eigenspectrum of the free fermion model. Based on the
numerical observations we formulate several conjectures. Using explicit
solutions of the associated nested Bethe-ansatz equations, guessed from an
analysis of the functional equations of the model, we provide evidence for a
part of them.Comment: 19 pages, no figure
Effective Field Theory of Triangular-Lattice Three-Spin Interaction Model
We discuss an effective field theory of a triangular-lattice three-spin
interaction model defined by the variables. Based on the
symmetry properties and the ideal-state graph concept, we show that the vector
dual sine-Gordon model describes the long-distance properties for ; we
then compare its predictions with the previous argument. To provide the
evidences, we numerically analyze the eigenvalue structure of the transfer
matrix for , and we check the criticality with the central charge of
the intermediate phase and the quantization condition of the vector charges.Comment: 4 pages, 3 figure
Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
The spectrum of the non-hermitian asymmetric XXZ-chain with additional
non-diagonal boundary terms is studied. The lowest lying eigenvalues are
determined numerically. For the ferromagnetic and completely asymmetric chain
that corresponds to a reaction-diffusion model with input and outflow of
particles the smallest energy gap which corresponds directly to the inverse of
the temporal correlation length shows the same properties as the spatial
correlation length of the stationary state. For the antiferromagnetic chain
with both boundary terms, we find a conformal invariant spectrum where the
partition function corresponds to the one of a Coulomb gas with only magnetic
charges shifted by a purely imaginary and a lattice-length dependent constant.
Similar results are obtained by studying a toy model that can be diagonalized
analytically in terms of free fermions.Comment: LaTeX, 26 pages, 1 figure, uses ioplppt.st
The Bethe ansatz as a matrix product ansatz
The Bethe ansatz in its several formulations is the common tool for the exact
solution of one dimensional quantum Hamiltonians. This ansatz asserts that the
several eigenfunctions of the Hamiltonians are given in terms of a sum of
permutations of plane waves. We present results that induce us to expect that,
alternatively, the eigenfunctions of all the exact integrable quantum chains
can also be expressed by a matrix product ansatz. In this ansatz the several
components of the eigenfunctions are obtained through the algebraic properties
of properly defined matrices. This ansatz allows an unified formulation of
several exact integrable Hamiltonians. We show how to formulate this ansatz for
a huge family of quantum chains like the anisotropic Heisenberg model,
Fateev-Zamolodchikov model, Izergin-Korepin model, model, Hubbard model,
etc.Comment: 4 pages and no figure
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