7,887 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
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
Asymmetric exclusion model with several kinds of impurities
We formulate a new integrable asymmetric exclusion process with
kinds of impurities and with hierarchically ordered dynamics.
The model we proposed displays the full spectrum of the simple asymmetric
exclusion model plus new levels. The first excited state belongs to these new
levels and displays unusual scaling exponents. We conjecture that, while the
simple asymmetric exclusion process without impurities belongs to the KPZ
universality class with dynamical exponent 3/2, our model has a scaling
exponent . In order to check the conjecture, we solve numerically the
Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found
the dynamical exponents 7/2 and 9/2 in these cases.Comment: to appear in JSTA
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
Non-contractible loops in the dense O(n) loop model on the cylinder
A lattice model of critical dense polymers is considered for the
finite cylinder geometry. Due to the presence of non-contractible loops with a
fixed fugacity , the model is a generalization of the critical dense
polymers solved by Pearce, Rasmussen and Villani. We found the free energy for
any height and circumference of the cylinder. The density of
non-contractible loops is found for and large . The
results are compared with those obtained for the anisotropic quantum chain with
twisted boundary conditions. Using the latter method we obtained for any
model and an arbitrary fugacity.Comment: arXiv admin note: text overlap with arXiv:0810.223
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
Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions
We investigate the interface dynamics of the two-dimensional stochastic Ising
model in an external field under helicoidal boundary conditions. At
sufficiently low temperatures and fields, the dynamics of the interface is
described by an exactly solvable high-spin asymmetric quantum Hamiltonian that
is the infinitesimal generator of the zero range process. Generally, the
critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang
universality class of critical behavior. We remark that a whole family of RSOS
interface models similar to the Ising interface model investigated here can be
described by exactly solvable restricted high-spin quantum XXZ-type
Hamiltonians.Comment: LaTeX2e, 15 pages, 1 figure, 40 references. This paper is dedicated
to Professor Silvio R. A. Salinas (IF/USP) on the occasion of his 70th
birthda
Entanglement and Quantum Phases in the Anisotropic Ferromagnetic Heisenberg Chain in the Presence of Domain Walls
We discuss entanglement in the spin-1/2 anisotropic ferromagnetic Heisenberg
chain in the presence of a boundary magnetic field generating domain walls. By
increasing the magnetic field, the model undergoes a first-order quantum phase
transition from a ferromagnetic to a kink-type phase, which is associated to a
jump in the content of entanglement available in the system. Above the critical
point, pairwise entanglement is shown to be non-vanishing and independent of
the boundary magnetic field for large chains. Based on this result, we provide
an analytical expression for the entanglement between arbitrary spins. Moreover
the effects of the quantum domains on the gapless region and for
antiferromagnetic anisotropy are numerically analysed. Finally multiparticle
entanglement properties are considered, from which we establish a
characterization of the critical anisotropy separating the gapless regime from
the kink-type phase.Comment: v3: 7 pages, including 4 figures and 1 table. Published version. v2:
One section (V) added and references update
- …