223 research outputs found

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

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

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
{{$\alpha_-$,$\alpha_+$,$\beta_-$,$\beta_+$}} are nonzero. A generalization of
the Baxter $T-Q$ equation that involves more than one independent $Q$ 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

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

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

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

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

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 ($t^{{1/3}}$), when compared with the normal
diffusive behavior ($t^{{1/2}}$). 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 $z$, for size $S \geq 0$ particles is extended to
the case $S<0$ and the KPZ result $z=3/2$ is predicted for all values of $S \in
{Z}$.Comment: 4 pages, 3 figure

### General Reaction-Diffusion Processes With Separable Equations for Correlation Functions

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

We study a one-dimensional class of reaction-diffusion models on a
$10-$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

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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