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

A Generalized Duality Transformation of the Anisotropic Xy Chain in a Magnetic Field

We consider the anisotropic $XY$ chain in a magnetic field with special boundary conditions described by a two-parameter Hamiltonian. It is shown that the exchange of the parameters corresponds to a similarity transformation, which reduces in a special limit to the Ising duality transformation.Comment: 6 pages, LaTeX, BONN-HE-93-4

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

Exactly Solvable Interacting Spin-Ice Vertex Model

A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of models includes in a special limit the standard six-vertex model. The exact solution of these models gives the first application of the matrix product ansatz introduced recently and applied successfully in the solution of quantum chains. The phase diagram and the free energy of the models are calculated in the thermodynamic limit. The models exhibit massless phases and our analyticaland numerical analysis indicate that such phases are governed by a conformal field theory with central charge $c=1$ and continuosly varying critical exponents.Comment: 14 pages, 11 figure

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

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

The Wave Functions for the Free-Fermion Part of the Spectrum of the SUq(N)SU_q(N) Quantum Spin Models

We conjecture that the free-fermion part of the eigenspectrum observed recently for the $SU_q(N)$ Perk-Schultz spin chain Hamiltonian in a finite lattice with $q=\exp (i\pi (N-1)/N)$ is a consequence of the existence of a special simple eigenvalue for the transfer matrix of the auxiliary inhomogeneous $SU_q(N-1)$ 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 ($q=\exp (2 i \pi/3)$), 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 $SU_q(2)$ case at $q=\exp(i2\pi/3)$ our numerical and analytical studies induce some conjectures for special rates of correlation functions.Comment: 25 pages and no figure

The phase diagram of the anisotropic Spin-1 Heisenberg Chain

We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum chain. In studing this model we aim to clarify controversials about the point where the massive Haldane phase appears.Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencode

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

Antiresonance and interaction-induced localization in spin and qubit chains with defects

We study a spin chain with an anisotropic XXZ coupling in an external field. Such a chain models several proposed types of a quantum computer. The chain contains a defect with a different on-site energy. The interaction between excitations is shown to lead to two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive quantum interference suppresses this decay. Numerical results confirm the analytical predictions.Comment: Updated versio