5,739 research outputs found
Generalization of the matrix product ansatz for integrable chains
We present a general formulation of the matrix product ansatz for exactly
integrable chains on periodic lattices. This new formulation extends the matrix
product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo
J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004)
4149-4182.)Comment: 5 pages. to appear in J. Phys. A: Math. Ge
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
Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product
Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional
periodic lattice. In this Matrix Product Ansatz, the components of the
eigenvectors of the ASEP Markov matrix can be expressed as traces of products
of non-commuting operators. We derive the relations between the operators
involved and show that they generate a quadratic algebra. Our construction
provides explicit finite dimensional representations for the generators of this
algebra.Comment: 16 page
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
On Matrix Product States for Periodic Boundary Conditions
The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.Comment: 7 pages, late
Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization
We study the influence of ferromagnetic and antiferromagnetic bond defects on
the ground-state energy of antiferromagnetic spin chains. In the absence of
translational invariance, the energy spectrum of the full Hamiltonian is
obtained numerically, by an iterative modification of the power algorithm. In
parallel, approximate analytical energies are obtained from a local-bond
approximation, proposed here. This approximation results in significant
improvement upon the mean-field approximation, at negligible extra
computational effort.Comment: 3 pages, 2 figures. Manuscript accepted by Journal of Magnetism and
Magnetic Materials, special issue for LAWMMM 2007 conferenc
On the density matrix for the kink ground state of higher spin XXZ chain
The exact expression for the density matrix of the kink ground state of
higher spin XXZ chain is obtained
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.
The Yang-Baxter equation for PT invariant nineteen vertex models
We study the solutions of the Yang-Baxter equation associated to nineteen
vertex models invariant by the parity-time symmetry from the perspective of
algebraic geometry. We determine the form of the algebraic curves constraining
the respective Boltzmann weights and found that they possess a universal
structure. This allows us to classify the integrable manifolds in four
different families reproducing three known models besides uncovering a novel
nineteen vertex model in a unified way. The introduction of the spectral
parameter on the weights is made via the parameterization of the fundamental
algebraic curve which is a conic. The diagonalization of the transfer matrix of
the new vertex model and its thermodynamic limit properties are discussed. We
point out a connection between the form of the main curve and the nature of the
excitations of the corresponding spin-1 chains.Comment: 43 pages, 6 figures and 5 table
Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
An ASEP with two species of particles and different hopping rates is
considered on a ring. Its integrability is proved and the Nested Algebraic
Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary
numbers of particles of each type, generalizing the results of Derrida and
Evans. We present also formulas for the total velocity of particles of a given
type and their limit for large size of the system and finite densities of the
particles.Comment: 14 page
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