56 research outputs found
Yangian description for decays and possible explanation of in the decay
In this letter, hadronic decay channels of light pseudoscalar mesons are
realized in Yangian algebra. In the framework of Yangian, we find that these
decay channels can be formulated by acting transition operators, composed of
the generators of Yangian, on the corresponding pseudoscalar mesons. This new
description of decays allows us to present a possible interpretation of the new
unknown particle in the decay : it is an entangled
state of and
Quantum algebra in the mixed light pseudoscalar meson states
In this paper, we investigate the entanglement degrees of pseudoscalar meson
states via quantum algebra Y(su(3)). By making use of transition effect of
generators J of Y(su(3)), we construct various transition operators in terms of
J of Y(su(3)), and act them on eta-pion-eta mixing meson state. The
entanglement degrees of both the initial state and final state are calculated
with the help of entropy theory. The diagrams of entanglement degrees are
presented. Our result shows that a state with desired entanglement degree can
be achieved by acting proper chosen transition operator on an initial state.
This sheds new light on the connect among quantum information, particle physics
and Yangian algebra.Comment: 9 pages, 3 figure
Integrable Matrix Product States from boundary integrability
We consider integrable Matrix Product States (MPS) in integrable spin chains
and show that they correspond to "operator valued" solutions of the so-called
twisted Boundary Yang-Baxter (or reflection) equation. We argue that the
integrability condition is equivalent to a new linear intertwiner relation,
which we call the "square root relation", because it involves half of the steps
of the reflection equation. It is then shown that the square root relation
leads to the full Boundary Yang-Baxter equations. We provide explicit solutions
in a number of cases characterized by special symmetries. These correspond to
the "symmetric pairs" and , where
in each pair the first and second elements are the symmetry groups of the spin
chain and the integrable state, respectively. These solutions can be considered
as explicit representations of the corresponding twisted Yangians, that are new
in a number of cases. Examples include certain concrete MPS relevant for the
computation of one-point functions in defect AdS/CFT.Comment: 33 pages, v2: minor corrections, references added, v3: minor
modifications, v4: minor modification
Yangian symmetry applied to Quantum chromodynamics
We review applications of Yangain symmetry to high-energy QCD phenomenology.
Some basic facts about high-energy QCD are recalled, in particular the
spinor-helicity form of scattering amplitudes, the scale evolution equations of
deep-inelastic scattering structure functions and the high-energy asymptotics
of scattering. As the working tool the Yangian symmetric correlators are
introduced and constructed in the framework of the Yangian algebra of
type. We present the application to the tree scattering amplitudes
and their iterative relation, to the parton splitting amplitudes and the
kernels of the scale evolution equations of structure functions and to the
equations describing the high-energy asymptotics of scattering.Comment: 48 pages, 5 figure
The hexagon in the mirror: the three-point function in the SoV representation
We derive an integral expression for the leading-order type I-I-I three-point
functions in the -sector of super Yang-Mills
theory, for which no determinant formula is known. To this end, we first map
the problem to the partition function of the six vertex model with a hexagonal
boundary. The advantage of the six-vertex model expression is that it reveals
an extra symmetry of the problem, which is the invariance under 90
rotation. On the spin-chain side, this corresponds to the exchange of the
quantum space and the auxiliary space and is reminiscent of the mirror
transformation employed in the worldsheet S-matrix approaches. After the
rotation, we then apply Sklyanin's separation of variables (SoV) and obtain a
multiple-integral expression of the three-point function. The resulting
integrand is expressed in terms of the so-called Baxter polynomials, which is
closely related to the quantum spectral curve approach. Along the way, we also
derive several new results about the SoV, such as the explicit construction of
the basis with twisted boundary conditions and the overlap between the orginal
SoV state and the SoV states on the subchains.Comment: 37 pages, 10 figure
Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models
with su spin and long-range non-constant interactions, whose
non-degenerate ground state is a Dicke state of su type. We evaluate in
closed form the reduced density matrix of a block of spins when the whole
system is in its ground state, and study the corresponding von Neumann and
R\'enyi entanglement entropies in the thermodynamic limit. We show that both of
these entropies scale as when tends to infinity, where the
coefficient is equal to in the ground state phase with
vanishing su magnon densities. In particular, our results show that none
of these generalized Lipkin-Meshkov-Glick models are critical, since when
their R\'enyi entropy becomes independent of the parameter
. We have also computed the Tsallis entanglement entropy of the ground state
of these generalized su Lipkin-Meshkov-Glick models, finding that it can
be made extensive by an appropriate choice of its parameter only when
. Finally, in the su case we construct in detail the phase
diagram of the ground state in parameter space, showing that it is determined
in a simple way by the weights of the fundamental representation of su.
This is also true in the su case; for instance, we prove that the region
for which all the magnon densities are non-vanishing is an -simplex in
whose vertices are the weights of the fundamental representation
of su.Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with
corrections and additional reference
Opérateurs de Heun, ansatz de Bethe et représentations de
Le prĂ©sent mĂ©moire contient deux articles reliĂ©s par le formalisme de l'ansatz de Bethe. Dans le premier article, l'opĂ©rateur de Heun de type Lie est identifiĂ© comme une spĂ©cialisation de la matrice de transfert d'un modĂšle de -Gaudin Ă un site dans un champ magnĂ©tique. Ceci permet de le diagonaliser Ă l'aide de l'ansatz de Bethe algĂ©brique modifiĂ©. La complĂ©tude du spectre est dĂ©montrĂ©e en reliant les racines de Bethe aux zĂ©ros des solutions polynomiales d'une Ă©quation diffĂ©rentielle de Heun inhomogĂšne. Le deuxiĂšme article aborde le sujet des reprĂ©sentations irrĂ©ductibles de l'algĂšbre de Lie dans la rĂ©duction . Cette maniĂšre de construire les reprĂ©sentations irrĂ©ductibles de porte une ambiguĂŻtĂ© qui empĂȘche de distinguer totalement les vecteurs de base, ce qui mĂšne Ă un problĂšme d'Ă©tiquette manquante. Dans cet esprit, l'algĂšbre des deux opĂ©rateurs fournissant cette Ă©tiquette est examinĂ©e. L'opĂ©rateur de degrĂ© 4 dans les gĂ©nĂ©rateurs de est diagonalisĂ© en se servant des techniques de l'ansatz de Bethe analytique.This Masterâs thesis contains two articles linked by the formalism of the Bethe ansatz. In the first article, the Lie-type Heun operator is identified as a specialization of the transfer matrix of a one-site BC-Gaudin model in a magnetic field. This allows its diagonalization by means of the modified algebraic Bethe ansatz. The completeness of the spectrum is proven by relating the Bethe roots to the zeros of the polynomial solutions of an inhomogeneous differential Heun equation. The second article deals with the subject of irreducible representations of the Lie algebra su(3) in the reduction su(3) â so(3) â so(2). This way of constructing the irreducible representations of su(3) carries an ambiguity in distinguishing the basis vectors, also known as a missing label problem. In this spirit, the algebra of the two operators providing the missing label is examined. The operator of degree 4 in the generators of su(3) is diagonalized using the techniques of the analytical Bethe ansatz
New Integrable Models from the Gauge/YBE Correspondence
We introduce a class of new integrable lattice models labeled by a pair of
positive integers N and r. The integrable model is obtained from the Gauge/YBE
correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r
index of a large class of SU(N) quiver gauge theories with the partition
function of 2d classical integrable spin models. The integrability of the model
(star-star relation) is equivalent with the invariance of the index under the
Seiberg duality. Our solution to the Yang-Baxter equation is one of the most
general known in the literature, and reproduces a number of known integrable
models. Our analysis identifies the Yang-Baxter equation with a particular
duality (called the Yang-Baxter duality) between two 4d N=1 supersymmetric
quiver gauge theories. This suggests that the integrability goes beyond 4d lens
indices and can be extended to the full physical equivalence among the IR fixed
points.Comment: 20 pages, 9 figure
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