143 research outputs found
Universal Low Temperature Asymptotics of the Correlation Functions of the Heisenberg Chain
We calculate the low temperature asymptotics of a function that
generates the temperature dependence of all static correlation functions of the
isotropic Heisenberg chain.Comment: Proceedings of the International Workshop "Recent Advances in Quantum
Integrable Systems" (Annecy, France
Coordinate Bethe Ansatz for Spin s XXX Model
We compute the eigenfunctions and eigenvalues of the periodic integrable spin
s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly
the Hamiltonian of the model. These results generalize what has been obtained
for spin 1/2 and spin 1 chains
Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
We present a generalization of the coordinate Bethe ansatz that allows us to
solve integrable open XXZ and ASEP models with non-diagonal boundary matrices,
provided their parameters obey some relations. These relations extend the ones
already known in the literature in the context of algebraic or functional Bethe
ansatz. The eigenvectors are represented as sums over cosets of the Weyl
group.Comment: typos corrected, references updated, accepted in J. Stat. Mec
Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
The one-dimensional problem of particles with contact interaction in the
presence of a tunable transmitting and reflecting impurity is investigated
along the lines of the coordinate Bethe ansatz. As a result, the system is
shown to be exactly solvable by determining the eigenfunctions and the energy
spectrum. The latter is given by the solutions of the Bethe ansatz equations
which we establish for different boundary conditions in the presence of the
impurity. These impurity Bethe equations contain as special cases well-known
Bethe equations for systems on the half-line. We briefly study them on their
own through the toy-examples of one and two particles. It turns out that the
impurity can be tuned to lift degeneracies in the energies and can create bound
states when it is sufficiently attractive. The example of an impurity sitting
at the center of a box and breaking parity invariance shows that such an
impurity can be used to confine asymmetrically a stationary state. This could
have interesting applications in condensed matter physics.Comment: 20 pages, 5 figures, version accepted for publication: some typos
corrected, references and comments adde
Triaxial quadrupole deformation dynamics in sd-shell nuclei around 26Mg
Large-amplitude dynamics of axial and triaxial quadrupole deformation in
24,26Mg, 24Ne, and 28Si is investigated on the basis of the quadrupole
collective Hamiltonian constructed with use of the constrained
Hartree-Fock-Bogoliubov plus the local quasiparticle random phase approximation
method. The calculation reproduces well properties of the ground rotational
bands, and beta and gamma vibrations in 24Mg and 28Si. The gamma-softness in
the collective states of 26Mg and 24Ne are discussed. Contributions of the
neutrons and protons to the transition properties are also analyzed in
connection with the large-amplitude quadrupole dynamics.Comment: 16 pages, 18 figures, submitted to Phys. Rev.
Precursors and Laggards: An Analysis of Semantic Temporal Relationships on a Blog Network
We explore the hypothesis that it is possible to obtain information about the
dynamics of a blog network by analysing the temporal relationships between
blogs at a semantic level, and that this type of analysis adds to the knowledge
that can be extracted by studying the network only at the structural level of
URL links. We present an algorithm to automatically detect fine-grained
discussion topics, characterized by n-grams and time intervals. We then propose
a probabilistic model to estimate the temporal relationships that blogs have
with one another. We define the precursor score of blog A in relation to blog B
as the probability that A enters a new topic before B, discounting the effect
created by asymmetric posting rates. Network-level metrics of precursor and
laggard behavior are derived from these dyadic precursor score estimations.
This model is used to analyze a network of French political blogs. The scores
are compared to traditional link degree metrics. We obtain insights into the
dynamics of topic participation on this network, as well as the relationship
between precursor/laggard and linking behaviors. We validate and analyze
results with the help of an expert on the French blogosphere. Finally, we
propose possible applications to the improvement of search engine ranking
algorithms
The Higher-Rank Askey-Wilson Algebra and Its Braid Group Automorphisms
We propose a definition by generators and relations of the rank
Askey-Wilson algebra for any integer , generalising the
known presentation for the usual case . The generators are indexed by
connected subsets of and the simple and rather small set of
defining relations is directly inspired from the known case of . Our first
main result is to prove the existence of automorphisms of
satisfying the relations of the braid group on strands. We also show the
existence of coproduct maps relating the algebras for different values of .
An immediate consequence of our approach is that the Askey-Wilson algebra
defined here surjects onto the algebra generated by the intermediate Casimir
elements in the -fold tensor product of the quantum group or, equivalently, onto the Kauffman bracket skein
algebra of the -punctured sphere. We also obtain a family of central
elements of the Askey-Wilson algebras which are shown, as a direct by-product
of our construction, to be sent to in the realisation in the -fold
tensor product of , thereby producing a large
number of relations for the algebra generated by the intermediate Casimir
elements
New integrable boundary conditions for the Ablowitz–Ladik model: From Hamiltonian formalism to nonlinear mirror image method
Using Sklyanin's classical theory of integrable boundary conditions, we use the Hamiltonian approach to derive new integrable boundary conditions for the Ablowitz–Ladik model on the finite and half infinite lattice. In the case of half infinite lattice, the special and new emphasis of this paper is to connect directly the Hamiltonian approach, based on the classical r-matrix, with the zero curvature representation and Bäcklund transformation approach that allows one to implement a nonlinear mirror image method and construct explicit solutions. It is shown that for our boundary conditions, which generalise (discrete) Robin boundary conditions, a nontrivial extension of the known mirror image method to what we call time-dependent boundary conditions is needed. A careful discussion of this extension is given and is facilitated by introducing the notion of intrinsic and extrinsic picture for describing boundary conditions. This gives the specific link between Sklyanin's reflection matrices and Bäcklund transformations combined with folding, in the case of non-diagonal reflection matrices. All our results reproduce the known Robin boundary conditions setup as a special case: the diagonal case. Explicit formulas for constructing multisoliton solutions on the half-lattice with our time-dependent boundary conditions are given and some examples are plotted
Multipartite information of free fermions on Hamming graphs
We investigate multipartite information and entanglement measures in the
ground state of a free-fermion model defined on a Hamming graph. Using the
known diagonalization of the adjacency matrix, we solve the model and construct
the ground-state correlation matrix. Moreover, we find all the eigenvalues of
the chopped correlation matrix when the subsystem consists of disjoint
Hamming subgraphs embedded in a larger one. These results allow us to find an
exact formula for the entanglement entropy of disjoint graphs, as well as for
the mutual and tripartite information. We use the exact formulas for these
measures to extract their asymptotic behavior in two distinct thermodynamic
limits, and find excellent match with the numerical calculations. In
particular, we find that the entanglement entropy admits a logarithmic
violation of the area law which decreases the amount of entanglement compared
to the area law scaling.Comment: 12 pages, 4 figures, v2: minor modification
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