7,423 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
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
Spectrum of a duality-twisted Ising quantum chain
The Ising quantum chain with a peculiar twisted boundary condition is
considered. This boundary condition, first introduced in the framework of the
spin-1/2 XXZ Heisenberg quantum chain, is related to the duality
transformation, which becomes a symmetry of the model at the critical point.
Thus, at the critical point, the Ising quantum chain with the duality-twisted
boundary is translationally invariant, similar as in the case of the usual
periodic or antiperiodic boundary conditions. The complete energy spectrum of
the Ising quantum chain is calculated analytically for finite systems, and the
conformal properties of the scaling limit are investigated. This provides an
explicit example of a conformal twisted boundary condition and a corresponding
generalised twisted partition function.Comment: LaTeX, 7 pages, using IOP style
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
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
Preventing Advanced Persistent Threats in Complex Control Networks
An Advanced Persistent Threat (APT) is an emerging attack against Industrial Control and Automation Systems, that is executed over a long period of time and is difficult to detect. In this context, graph theory can be applied to model the interaction among nodes and the complex attacks affecting them, as well as to design recovery techniques that ensure the survivability of the network. Accordingly, we leverage a decision model to study how a set of hierarchically selected nodes can collaborate to detect an APT within the network, concerning the presence of changes in its topology. Moreover, we implement a response service based on redundant links that dynamically uses a secret sharing scheme and applies a flexible routing protocol depending on the severity of the attack. The ultimate goal is twofold: ensuring the reachability between nodes despite the changes and preventing the path followed by messages from being discovered.Universidad de MĂĄlaga. Campus de Excelencia Internacional AndalucĂa Tech
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
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
Integrability of a disordered Heisenberg spin-1/2 chain
We investigate how the transition from integrability to nonintegrability
occurs by changing the parameters of the Hamiltonian of a Heisenberg spin-1/2
chain with defects. Randomly distributed defects may lead to quantum chaos. A
similar behavior is obtained in the presence of a single defect out of the
edges of the chain, suggesting that randomness is not the cause of chaos in
these systems, but the mere presence of a defect.Comment: 4 pages, 4 figure
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
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