223 research outputs found

    Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

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    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

    Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain

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    We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters {{α\alpha_-,α+\alpha_+,β\beta_-,β+\beta_+}} are nonzero. A generalization of the Baxter TQT-Q equation that involves more than one independent QQ is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.Comment: 6 pages, Latex; contribution to the XVth International Colloquium on Integrable Systems and Quantum Symmetries, Prague, June 2006. To appear in Czechoslovak Journal of Physics (2006); (v2) Typos corrected and a new line added in the Acknowledgments sectio

    Phase diagram of a coupled tetrahedral Heisenberg model

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    The phase diagram of a coupled tetrahedral Heisenberg model is obtained. The quantum chain has a local gauge symmetry and its eigenspectrum is obtained by the composition of the eigenspectra of spin-1/2 XXZ chains with arbitrary distribution of spin-3/2 impurities. The phase diagram is quite rich with an infinite number of phases with ferromagnetic, antiferromagnetic or ferrimagnetic order. In some cases the ground state and the low lying eigenlevels of the model can be exactly calculated since they coincide with the eigenlevels of the exactly integrable XXZ chain. The thermodynamical properties of the model at low temperatures is also studied through finite-size analysis.Comment: 23 pages, 15 figure

    Entanglement in quantum computers described by the XXZ model with defects

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    We investigate how to generate maximally entangled states in systems characterized by the Hamiltonian of the XXZ model with defects. Some proposed quantum computers are described by such model. We show how the defects can be used to obtain EPR states and W states when one or two excitations are considered.Comment: 4 pages, 1 figur

    XXZ spin chain in transverse field as a regularization of the sine-Gordon model

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    We consider here XXZ spin chain perturbed by the operator sigma^x (``in transverse field'') which is a lattice regularization of the sine-Gordon model. This can be shown using conformal perturbation theory. We calculated mass ratios of particles which lie in a discrete part of the spectrum and obtained results in accord with the DHN formula and in disagreement with recent calculations in literature based on numerical Bethe Ansatz and infinite momentum frame methods. We also analysed a short distance behavior of this states (UV or conformal limit). Our result for conformal dimension of the second breather state is different from the conjecture in [Klassen and Melzer, Int. J. Mod. Phys. A8, 4131 (1993)] and is consistent with this paper for other states.Comment: 7 pages, REVTeX, 6 figures, to appear in Phys. Rev.

    Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability

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    The super Yang-Mills duals of open strings attached to maximal giant gravitons are studied in perturbation theory. It is shown that non-BPS baryonic excitations of the gauge theory can be studied within the paradigm of open quantum spin chains even beyond the leading order in perturbation theory. The open spin chain describing the two loop mixing of non-BPS giant gravitons charged under an su(2) of the so(6) R symmetry group is explicitly constructed. It is also shown that although the corresponding open spin chain is integrable at the one loop order, there is a potential breakdown of integrability at two and higher loops. The study of integrability is performed using coordinate Bethe ansatz techniques.Comment: 28 pages. References added in revised versio

    Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes

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    Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the restriction of relative ordering of the particles is partially brocken. The models probing these effects are those of biased diffusion of particles having size S=0,1,2,..., or an effective negative "size" S=-1,-2,..., in units of lattice space. Our numerical simulations show that irrespective of the range of the hard-core potential, as long some relative ordering of particles are kept, we find suitable sliding-tag correlation functions whose fluctuations growth with time anomalously slow (t1/3t^{{1/3}}), when compared with the normal diffusive behavior (t1/2t^{{1/2}}). These results indicate that the critical behavior of these stochastic models are in the Kardar-Parisi-Zhang (KPZ) universality class. Moreover a previous Bethe-ansatz calculation of the dynamical critical exponent zz, for size S0S \geq 0 particles is extended to the case S<0S<0 and the KPZ result z=3/2z=3/2 is predicted for all values of SZS \in {Z}.Comment: 4 pages, 3 figure

    General Reaction-Diffusion Processes With Separable Equations for Correlation Functions

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    We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on any type of lattice. We also show that under these conditions the evolution equations for two point functions at different times are also closed. As an example we introduce a class of two species models which may be useful for the description of voting processes or the spreading of epidemics.Comment: 17 pages, Latex, No figure

    Solution of a class of one-dimensional reaction-diffusion models in disordered media

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    We study a one-dimensional class of reaction-diffusion models on a 1010-parameters manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behaviour of the density and correlation functions for {\it quenched} disordered systems. The {\it quenched} disorder consists of disconnected domains of reaction. We first consider the case where the disorder comprizes a superposition, with different probabilistic weights, of finite segments, with {\it periodic boundary conditions}. We then pass to the case of finite segments with {\it open boundary conditions}: we solve the ordered dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and investigate further its disordered version.Comment: 11 pages, no figures. To appear in Phys.Rev.

    Magnetization-plateau state of the S=3/2 spin chain with single ion anisotropy

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    We reexamine the numerical study of the magnetized state of the S=3/2 spin chain with single ion anisotropy D(> 0) for the magnetization M=M_{S}/3, where M_{S} is the saturation magnetization. We find at this magnetization that for D<D_{c1}=0.387 the system is critical and the magnetization plateau does not appear. For D > D_{c1}, the parameter region is divided into two parts D_{c1} < D < D_{c2}=0.943 and D_{c2} < D. In each region, the system is gapful and the M=M_{S}/3 magnetization plateau appears in the magnetization process. From our numerical calculation, the intermediate region D_{c1} < D < D_{c2} should be characterized by a magnetized valence-bond-solid state.Comment: 6 pages, 8 figure
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