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

Cerenkov angle and charge reconstruction with the RICH detector of the AMS experiment

The Alpha Magnetic Spectrometer (AMS) experiment to be installed on the International Space Station (ISS) will be equipped with a proximity focusing Ring Imaging Cerenkov (RICH) detector, for measurements of particle electric charge and velocity. In this note, two possible methods for reconstructing the Cerenkov angle and the electric charge with the RICH, are discussed. A Likelihood method for the Cerenkov angle reconstruction was applied leading to a velocity determination for protons with a resolution of around 0.1%. The existence of a large fraction of background photons which can vary from event to event, implied a charge reconstruction method based on an overall efficiency estimation on an event-by-event basis.Comment: Proceedings submitted to RICH 2002 (Pylos-Greece

The Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. We present initially the solution of the problem when an arbitrary mixture of molecules, each of then having an arbitrary size ($s=0,1,2, ...$) in units of lattice spacing, diffuses asymmetrically on the lattice. The solution of the more general problem where we have | the diffusion of particles belonging to $N$ distinct class of particles ($c=1, ..., N$), with hierarchical order, and arbitrary sizes is also solved. Our matrix product {\it ansatz} asserts that the amplitudes of an arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed by a product of matrices. The algebraic properties of the matrices defining the {\it ansatz} depend on the particular associated Hamiltonian. The absence of contradictions in the algebraic relations defining the algebra ensures the exact integrability of the model. In the case of particles distributed in $N>2$ classes, the associativity of the above algebra implies the Yang-Baxter relations of the exact integrable model.Comment: 42 pages, 1 figur

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

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly $c$ of the underlying conformal field theory governing the long distance physics of the quantum chain. We studied analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models ($Q = 2$; 3 and 4), the XXZ quantum chain and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes its finite-size behavior already detects the universality class of quantum critical behavior.Comment: 5 pages, 5 figure

Exact solutions of exactly integrable quantum chains by a matrix product ansatz

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrix product ansatz that asserts that those amplitudes are given in terms of a matrix product. The eigenvalue equation for the Hamiltonian define the algebraic properties of the matrices defining the amplitudes. The existence of a consistent algebra imply the exact integrability of the model. The matrix product ansatz we propose allow an unified and simple formulation of several exact integrable Hamiltonians. In order to introduce and illustrate this ansatz we present the exact solutions of several quantum chains with one and two global conservation laws and periodic boundaries such as the XXZ chain, spin-1 Fateev-Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc. Formulation of the matrix product ansatz for quantum chains with open ends is also possible. As an illustration we present the exact solution of an extended XXZ chain with $z$-magnetic fields at the surface and arbitrary hard-core exclusion among the spins.Comment: 57 pages, no figure

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 $s = 0,1,2,...$, 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 $z$ 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

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