5,548 research outputs found
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
Excited states in the twisted XXZ spin chain
We compute the finite size spectrum for the spin 1/2 XXZ chain with twisted
boundary conditions, for anisotropy in the regime , and
arbitrary twist . The string hypothesis is employed for treating
complex excitations. The Bethe Ansatz equtions are solved within a coupled
non-linear integral equation approach, with one equation for each type of
string. The root-of-unity quantum group invariant periodic chain reduces to the
XXZ_1/2 chain with a set of twist boundary conditions (,
an integer multiple of ). For this model, the restricted
Hilbert space corresponds to an unitary conformal field theory, and we recover
all primary states in the Kac table in terms of states with specific twist and
strings.Comment: 16 pages, Latex; added discussion on quantum group invariance and
arbitrary magnon numbe
On the spin-liquid phase of one dimensional spin-1 bosons
We consider a model of one dimensional spin-1 bosons with repulsive
density-density interactions and antiferromagnetic exchange. We show that the
low energy effective field theory is given by a spin-charge separated theory of
a Tomonaga-Luttinger Hamiltonian and the O(3) nonlinear sigma model describing
collective charge and spin excitations respectively. At a particular ratio of
the density-density to spin-spin interaction the model is integrable, and we
use the exact solutions to provide an independent derivation of the low energy
effective theory. The system is in a superfluid phase made of singlet pairs of
bosons, and we calculate the long-distance asymptotics of certain correlation
functions.Comment: 17 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 , the tensor
product of auxiliary spaces. By changing the basis in , 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
Simplified Calculation of Boundary S Matrices
The antiferromagnetic Heisenberg spin chain with N spins has a sector with
N=odd, in which the number of excitations is odd. In particular, there is a
state with a single one-particle excitation. We exploit this fact to give a
simplified derivation of the boundary S matrix for the open antiferromagnetic
spin-1/2 Heisenberg spin chain with diagonal boundary magnetic fields.Comment: 8 pages, LaTeX, no figure
Mixed Heisenberg Chains. I. The Ground State Problem
We consider a mechanism for competing interactions in alternating Heisenberg
spin chains due to the formation of local spin-singlet pairs. The competition
of spin-1 and spin-0 states reveals hidden Ising symmetry of such alternating
chains.Comment: 7 pages, RevTeX, 4 embedded eps figures, final versio
Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.
We present a complete study of boundary bound states and related boundary
S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our
approach is based partly on the bootstrap procedure, and partly on the explicit
solution of the inhomogeneous XXZ model with boundary magnetic field and of the
boundary Thirring model. We identify boundary bound states with new ``boundary
strings'' in the Bethe ansatz. The boundary energy is also computed.Comment: 25 pages, harvmac macros Report USC-95-001
A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
We propose a dynamical matrix product ansatz describing the stochastic
dynamics of two species of particles with excluded-volume interaction and the
quantum mechanics of the associated quantum spin chains respectively. Analyzing
consistency of the time-dependent algebra which is obtained from the action of
the corresponding Markov generator, we obtain sufficient conditions on the
hopping rates for identifing the integrable models. From the dynamical algebra
we construct the quadratic algebra of Zamolodchikov type, associativity of
which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are
obtained directly from the dynamical matrix product ansatz.Comment: 19 pages Late
A deformed analogue of Onsager's symmetry in the XXZ open spin chain
The XXZ open spin chain with general integrable boundary conditions is shown
to possess a q-deformed analogue of the Onsager's algebra as fundamental
non-abelian symmetry which ensures the integrability of the model. This
symmetry implies the existence of a finite set of independent mutually
commuting nonlocal operators which form an abelian subalgebra. The transfer
matrix and local conserved quantities, for instance the Hamiltonian, are
expressed in terms of these nonlocal operators. It follows that Onsager's
original approach of the planar Ising model can be extended to the XXZ open
spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected,
clarifications in the text; v3: minor changes in references, version to
appear in JSTA
Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
We propose a set of conventional Bethe Ansatz equations and a corresponding
expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ
quantum spin chain with nondiagonal boundary terms, provided that the boundary
parameters obey a certain linear relation.Comment: 11 pages, LaTeX; amssymb, amsmath, no figures; v2: citation adde
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