Anomalous Gauge Boson Couplings in the e^+ e^- -> ZZ Process

We discuss experimental aspects related to the $\mathrm{e^+ e^-} \to \mathrm{Z}\mathrm{Z}$ process and to the search for anomalous ZZV couplings (V$= \mathrm{Z}, \gamma$) at LEP2 and future $\mathrm{e^+ e^-}$ colliders. We present two possible approaches for a realistic study of the reaction and discuss the differences between them. We find that the optimal method to study double Z resonant production and to quantify the presence of anomalous couplings requires the use of a complete four-fermion final-state calculation.Comment: 28 pages, 12 figures, final version for Phys. Rev.

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 $\Delta$). Our results indicate universal properties for all these chains. The whole phase, $1>\Delta>-1$, where the models change from ferromagnetic $( \Delta=1 )$ to ferrimagnetic $(\Delta=-1)$ 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

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 XX-model with boundaries. Part III:Magnetization profiles and boundary bound states

We calculate the magnetization profiles of the $\sigma_j^x$ and $\sigma_j^z$ operators for the XX-model with hermitian boundary terms. We study the profiles on the finite chain and in the continuum limit. The results are discussed in the context of conformal invariance. We also discuss boundary excitations and their effect on the magnetization profiles.Comment: 30 pages, 3 figure

Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions

We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalised by the `commuting transfer matrices' method. {}From the exact solution we obtain an independent derivation of the interfacial tension of the six-vertex model in the anti-ferroelectric phase. The nature of the corresponding integrable boundary condition on the $XXZ$ spin chain is also discussed.Comment: 18 pages, LaTeX with 1 PostScript figur

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, $t-J$ model, Hubbard model, etc.Comment: 4 pages and no figure

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

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

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\it J. Phys. A: Math. Gen.} \textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\it Commun. Math. Phys.}, \textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.Comment: 24 pages; minor typos are correcte