V. Caudrelier:
Electronic properties of a junction of quantum wires in the presence
of a transverse magnetic field
Using techniques of bosonization recently developed for star-graphs
of quantum wires combined with a new systematic method of computing
the total scattering matrix of an arbitrary quantum graphs,
we show that the Tomonaga-Luttinger model on an arbitrary graph is integrable. Using this,
we provide some exact results for the conductance and the current-
current correlation functions for the Tomonaga-Luttinger model on a
ring in the presence of an external magnetic field.
Pdf file of the presentation
J.S. Caux:
In- and out-of-equilibrium dynamics of integrable models
The application of the theory of integrably models to the
calculation of dynamical correlation functions of systems
such as quantum spin chains and low-dimensional atomic gases
has made much progress in recent years. The first part of this
talk will review some recent results on Heisenberg spin chains
and bosonic atomic gases, providing an introduction to the
underlying theory but also highlighting a number of new experimental
applications. The second part of the talk will be concerned
with the nonequilibrium dynamics of interacting quantum systems
after a sudden change in one of the system's parameters (quench).
A new method based on integrability will be presented, allowing the study
of such classes of problems.
Pdf file of the presentation
Keynote version of the presentation
T. Deguchi:
Correlation functions of the integrable spin-s XXZ
spin chains and some related topics
An exact derivation of the multiple-integral representations for the
correlation function with arbitrary entries is presented for the integrable
higher-spin XXZ spin chains in a massless regime. In particular, some new
techniques in the quantum inverse scattering problem are illustrated by
which we derive the multiple-integral representations explicitly.
Furthermore, some possible applications of the QISP techniques such as to
the QISP of superintegrable chiral Potts model are also discussed.
Pdf file of the presentation
V.K. Dobrev:
Intertwining Operator Realization of Non-Relativistic Holography
Pdf file of the presentation
A. Doikou:
Novel family of representations for the Temperley-Lieb algebras
We introduce a novel family of representations of the (boundary)
Temperley-Lieb algebra. The underlying symmetry algebra is also examined,
and it is shown that there exist non trivial quantum algebraic
realizations
that exactly commute with the novel representations.
L. Feher:
Ruijsenaars duality in the framework of symplectic reduction
The duality relation among `Calogero type' integrable many-body systems
discovered by Ruijsenaars requires that systems (i) and (ii) are in
duality if the action variables of system (i) are the particle positions
of system (ii) and vice versa. We review our recent work on the group
theoretical origin of Ruijsenaars' duality.
Pdf file of the presentation
O. Foda:
XXZ and KP
Using Slavnov's scalar product, one can show that each XXZ
Bethe eigenstate corresponds to a polynomial KP tau function.
Next, using Krichever's map, one can extend the above to a
correspondence between each XXZ Bethe eigenstate and a set of
algebraic geometric data. I would like to talk about what is
known about the above XXZ/KP, or equivalently, representation
theory/algebraic geometry correspondence.
A. Foerster:
Exactly solvable models for Bose-Einstein condensates
We investigate some Bethe ansatz integrable models in the
context of ultracold atom systems. First we briefly discuss the
integrability, mathematical and physical properties of some exactly
solvable models related to Bose-Einstein condensates.
Then we extend our discussion to the fermionic case. In particular,
we analyze the two-component attractive Fermi gas with polarization
in external fields. This model was solved long ago by Yang and
Gaudin through Bethe ansatz methods. Here we explore this solution
to study the precise nature of pairing and quantum phase transitions
in this model, and obtain the critical fields and the phase diagrams
in the weak and strong coupling regimes, capturing the nature of the
magnetic effects and quantum phase transitions in 1D interacting
fermions with population imbalance.
Pdf file of the presentation
A. Fring:
Antilinear deformations of integrable systems
A brief introduction to non-Hermitian Hamiltonian systems
with real eigenvalue spectra will be presented. It will be argued
that systems possessing an antilinear symmetry, such as
for instance PT (simultaneous parity and time reversal),
are quasi/pseudo Hermitian with real eigenvalue spectra and possess
a consistent quantum mechanical framework. The general framework
will be applied to some integrable models, such a quantum spin chains,
classical integrable systems associated to differential equations and
Calogero-Moser-Sutherland models. We present some recent results.
Pdf file of the presentation
A. Gainutdinov:
From an affine Temperley-Lieb algebra to non-rational non-chiral logarithmic CFT
We study an affine Temperley-Lieb algebra action on a periodic spin-chain of XX-type
with alternating twist conditions. Scaling limit of Fourier image for periodic Temperley-Lieb
(TL) generators gives a non-chiral (left and right) Virasoro algebra with c=-2 which defines a
non-rational non-chiral logarithmic CFT with infinitely many primary fields. Our main result on
the lattice part is a theorem on the (maximum) centralizer for the periodic TL. In particular,
the loop sl(2) symmetry (found by Deguchi, Fabricius and McCoy) of XX-hamiltonian is realized as
a subalgebra in the affine version of the centralizer. The theorem allows to obtain a decomposition
of the spin-chain into indecomposable modules over the periodic TL with non-trivial Jordan blocks
for the hamiltonian. The modules are of two-strands Feigin-Fuchs type (for Virasoro) in contrast
to the standard ones of Verma-type studied by Graham and Lehrer. The scaling limit of the indecomposables
on the lattice gives non-chiral versions of the staggered modules over chiral Virasoro algebra with
non-diagonalizable L_0. We thus obtain a full description of field content w.r.t. left and right
Virasoro in the non-rational non-chiral logarithmic theory.
J.F. Gomes:
Negative Even Grade mKdV Hierarchy and its soliton Solutions
An algebraic construction for the negative even mKdV hierarchy
giving rise to time evolutions associated to even graded Lie
algebraic structure is proposed. Explicit and systematic solutions
for the whole negative even grade equations. are constructed by a
modification of the dressing method which incorporates a non-trivial
vacuum configuration and deformed vertex operators for \hat{sl}(2).
Pdf file of the presentation
F. Göhmann:
Correlation functions of the integrable isotropic spin-1 chain
at finite temperature
We have derived a multiple integral representation for
the density matrix of the integrable isotropic spin-1 chain
in the thermodynamic limit. The results is valid at finite
temperature and includes a longitudinal magnetic field.
Pdf file of the presentation
N. Iorgov:
Spin operator matrix elements
in the superintegrable chiral Potts quantum chain
Pdf file of the presentation
M. Jimbo:
One point functions of descendants in the sine-Gordon model
Vacuum expectation values (VEVs) of local fields in
integrable field theory are important quantities carrying non-
perturbative information of the model.
Making use of a fermionic structure in the six vertex model,
we examine its continuum limit and
formulate conjectures about the VEVs of exponential fields and their
descendants in the sine-Gordon model. This is a joint work with F.
Smirnov and T. Miwa.
M. Karowski:
The form factor program: SU(N) and O(N) models
Pdf file of the presentation
N. Kitanine:
Trigonometric SOS model with DWBC and spin chains with non-diagonal boundaries
We compute the partition function of the trigonometric SOS model with one
reflecting end and domain wall type boundary conditions. We show that in this case,
instead of a sum of determinants obtained by Rosengren for the SOS model on a square
lattice without reflection, the partition function can be represented as a single Izergin
determinant. This result is crucial for the study of the Bethe vectors of the spin chains
with non-diagonal boundary terms.
Pdf file of the presentation
A. Klümper:
Spectral properties of quantum spin chains and Chalker-Coddington-networks
of Temperley-Lieb type
We determine the spectrum of a class of quantum spin chains of Temperley-Lieb
(TL) type by utilizing the concept of TL-equivalence with the spin-1/2 XXZ-
model as a reference system. We consider open boundary conditions and in
particular periodic boundary conditions. For both types of boundaries the
identification with XXZ-spectra is performed within isomorphic representations
of the underlying Temperley-Lieb algebra.
For open boundaries the spectra of these models differ from the spectrum of
the related XXZ-chain only in the multiplicities of the eigenvalues. The
periodic case is rather different. Here we show how the spectrum is obtained
sectorwise from the spectrum of globally twisted XXZ-chains via the
construction of appropriate reference states.
As applications we present:
(i) the complete treatment of the thermodynamics of two 3-state quantum spin
chains with su(3) and sl(2|1) symmetry (gapped and critical, resp.),
(ii) all scaling dimensions and logarithmic corrections for all low-lying
excitations of the critical sl(2|1)-invariant spin chain corresponding to
a Chalker-Coddington-network for the quantum spin Hall effect.
Pdf file of the presentation
K. Kozlowski:
Long-time/long-distance asymptotics of the two-point
functions in the non-linear Schödinger model
I will adress the problem of computing the long-time/long-distance
asymptotics of the two-point functions in the non-linear Schödinger model.
More precisely, I will discuss a method that allows one, starting from the form
factor series expansion, to construct the asymptotic series in the long-distance,
long-time regime. The key point of this analysis is the interpretation of the
two-point function as a multidimensional generalization of a determinant of an
integrable integral operator. Using Riemann-Hilbert problem based techniques,
we are able to provide a method for the asymptotic analysis of such objects,
in particular a constructive way to build the asymptotic series.
This is a joint work with Kitanine, Maillet, Slavnov and Terras.
Pdf file of the presentation
A. Kundu:
Nonultralocal Quantum Algebra and 1D Anyonic Quantum Integrable Models
Based on the braided Yang-Baxter equation a novel nonultralocal extention of the quantum
algebra is proposed and through its realization new quantum integrable and Bethe ansatz solvable
nonultralocal sine-Gordon and an 1D anyonic derivative nonlinear Schrodinger (DNLS) model,
realized through a novel nonultralocal q-oscillator, are constructed.
At q → 1 limit we obtain a new type of 1D anyonic algebra, which is used for constructing
quantum integrable anyonic lattice and field models. The lattice model is a nearest neighbor
interacting hard-core anyonic operator model, while the field model yields a new anyonic NLS
model.
The anyonic NLS and DNLS models at their N-particle sector produce the exactly solvable
1D anyon gas models interacting through δ-function and
δ'-function potentials,
discovering thus the important missing link between the solvable well known interacting anyon
gases and their corresponding integrable nonultralocal quantum field models.
Pdf file of the presentation
J.M. Maillet:
Asymptotic behavior of correlation functions : the Bethe ansatz viewpoint
Pdf file of the presentation
V. Mangazeev:
Correlations in the 2D Ising model and Painleve VI
We derive Toda-type recurrence relations for generalized diagonal correlation
functions in the two-dimensional Ising model, using an earlier connection between diagonal
form factor expansions and tau-functions within Painleve VI theory, originally discovered
by Jimbo and Miwa. We
also study the Toeplitz matrix representation for such generalized correlations.
Pdf file of the presentation
N. Manojlovic:
Symmetries of spin systems and Birman-Wenzl-Murakami algebra
We consider integrable open spin chains related to the quantum affine
algebras Uq(\hat{o(3)}) and
Uq(A2(2)). We discuss the symmetry
algebras of these chains with the local C3 space related to the
Birman-Wenzl-Murakami algebra. The symmetry algebra and the Birman-Wenzl-Murakami
algebra centralize each other in the representation space
H = ⊗1N C3 of the system, and this determines the
structure of the spin system spectra. Consequently,
the corresponding multiplet structure of the energy spectra is obtained.
Pdf file of the presentation
C. Matsui:
Correlation functions of quantum integrable spin chains with boundaries
Computation of correlation functions is one of main interests in
studying integrable systems. We derived correlation functions of
quantum integrable spin chains, especially higher spin chains,
with boundaries. Application to non-equilibrium systems of these
systems are also indicated by choosing appropriate boundaries.
Pdf file of the presentation
B. McCoy:
The many representations of the Ising form factors.
Ising form factors are characterized by:
1) explicit integrals;
2) expansions in terms of hypergeometric functions of modulus k;
3) expansions in terms of theta functions of nome q.
We present new results for the modulus and nome expansions,
demonstrate their equivalence and discuss their modular
transformation properties.
Pdf file of the presentation
A. Mikovic:
Category theory and quantum integrable systems
We review the category theory formulation of the Yang-Baxter equation
and the Zamolodchikov tetrahedron
equation and explain the role 2-groups can play for quantum integrable systems.
J.L. Miramontes:
The relativistic avatars of giant magnons.
The motion of strings on symmetric space target spaces underlies
the integrability of the AdS/CFT correspondence. Although the relevant
theories, whose excitations are giant magnons, are non-relativistic they are
classically equivalent, via the Polhmeyer reduction, to a family of
relativistic integrable Želd theories known as symmetric space sine-Gordon
(SSSG) theories. We will review their main features and a recent proposal
for the S-matrix formulation of the SSSG theories corresponding to complex
projective spaces.
Pdf file of the presentation
A. Molev:
The MacMahon Master Theorem and higher Sugawara operators
We prove an analogue of the MacMahon Master Theorem for the
right quantum superalgebras. In particular, we obtain a new and
simple proof of this theorem for the right quantum algebras. The
theorem is then used to construct higher order Sugawara operators
for the affine Lie superalgebra \hat gl(m|n) in an explicit form.
The operators are elements of a completed universal enveloping
algebra of \hat gl(m|n) at the critical level. They occur as the
coefficients in the expansion of a noncommutative Berezinian and
as the traces of powers of generator matrices. The same
construction yields higher Hamiltonians for the Gaudin model
associated with the Lie superalgebra gl(m|n).
This is joint work with Eric Ragoucy.
Pdf file of the presentation
E. Mukhin:
A generalization of Shapiro-Shapiro conjecture.
We use the Bethe ansatz method for the XXX model to prove the following
generalization of the B. and M. Shapiro conjecture in real algebraic geometry:
If the coefficients of the discrete Wronskian with pure imaginery step 2i of a set of
quasi-exponentials with real exponents are real and all roots of the Wronskian have
imaginery part at most 1, then the complex span of this set of quasi-exponentials has
a basis consisting of quasi-exponentials with real coefficients.
It is a joint work with V. Tarasov and A. Varchenko.
Pdf file of the presentation
S. Pakuliak:
Universal Bethe Ansatz and scalar products of Bethe vectors
Universal off-shell Bethe vectors in terms of the Drinfeld
(current) realization of the quantum affine algebra
Uq(\hat{gl}N) are considered. The ordering properties of the
product of the transfer matrix and these vectors are investigated.
The problem of calculation the scalar products of the Bethe vectors
using this representation is discussed.
Pdf file of the presentation
B. Pozsgay:
The exact g-function: Proofs and new results
We consider O(1) pieces to the free energy of (continuum) Bethe Ansatz
systems with boundaries. In relativistic models these contributions are given
by the exact g-function. In the framework of Thermodynamic Bethe Ansatz we
explain all previous results on the g-function in both massive and massless models.
In addition, we present a new formula which
applies to massless theories with arbitrary diagonal scattering in the bulk.
Y.H. Quano:
A vertex operator approach for form factors of Belavin's (Z/nZ)-symmetric model
Belavin's Z/nZ-symmetric model is considered on the basis of
bosonization of vertex operators in the A(1)n-1 model and vertex-face transformation.
Free field representations of nonlocal tail operators are constructed for off diagonal matrix
elements with respect to the ground state sectors. As a result, integral formulae for form
factors of any local operators in the Z/nZ-symmetric model can be
obtained, in principle.
Pdf file of the presentation
F. Ravanini:
T.B.A.
Pdf file of the presentation
I. Roditi:
Exactly solvable models for molecular Bose-Einstein Condensates
We construct a family of triatomic models for heteronuclear and
homonuclear molecular Bose-Einstein condensates. We show that these
new generalized models are exactly solvable through the algebraic
Bethe ansatz method and derive their corresponding Bethe ansatz
equations and energies.
M. Rossi:
Integrability in N=4 SYM: the non linear integral equation approach
Integrability is an essential tool in order to compute anomalous dimensions in N=4 SYM.
Bethe Ansatz equations are equivalent to non linear integral equations, which appears useful
in order to study states described by a large number of Bethe roots. I will review results
based on the use of the non linear integral equation in the sl(2) sector of
N=4 SYM and discuss applications of our techniques to more general cases.
Pdf file of the presentation
V. Roubtsov:
Elliptic Sklyanin algebras and Cremona transformations
Pdf file of the presentation
D. Simon:
Weak asymmetry regime of the exclusion process of the ring through Bethe Ansatz
The exclusion process is one of the simplest transport models of
out-of-equilibrium statistical physics. The computation of the distribution of
the current in this system can be performed through the Bethe Ansatz. However,
the weak asymmetry limit of this process is very different from the usual scalings
in spin chains : I will show the main properties of this limit of how
it gives new types of interesting results for integrable models.
Pdf file of the presentation
M. Staudacher:
A Shortcut to the Q-Operator
I will discuss a novel construction of Baxter's Q-operator
for the XXX spin chain. This is motivated by the need to understand
the Q-operators appearing in the Y-system of AdS/CFT.
M. Takahashi:
Correlation function and simplified TBA equations for XXZ chain
The calculation of the correlation functions of Bethe ansatz solvable models
is very difficult problem. Among these solvable models spin 1/2 XXX chain has
been investigated for a long time. Even for this model only the nearest
neighbor and the second neighbor correlations were known.
In 1990's Kyoto group gave multiple integral formula for the general
correlations.
But the integration of this formula is also very difficult problem.
Recently these integrals are decomposed
to products of one dimensional integrals and
correlation functions are expressed by Log[2] and Riemann's zeta functions
with odd integer argument Zeta[3], Zeta[5], Zeta[7],....
We can calculate density matrix of successive seven sites. This means that all
correlations in successive 7 sites can be calculated. These method can
be extended to
XXZ chain.
New thermodynamic Bethe ansatz equation for XXZ chain is derived.
This is quite different
with Yang-Yang type TBA equations and contains only one unknown function.
This equation is very useful to get the high temperature expansion.
Pdf file of the presentation
C. Young:
Jordan blocks of representations of quantum affine sl2.
Quantum affine algebras are a key ingredient in many integrable models,
but much about their rich representation theory remains to be understood.
In this talk I present some recent work (1004.2321 [math.QA]) on the structure of
standard modules of quantum affine sl(2). Standard modules are essentially tensor
products of fundamental representations. When these tensor factors are taken at
coincident rapidity, the action of the Cartan subalgebra generators in
Drinfel'd's current presentation becomes non-trivial, due to the formation of
Jordan blocks. I describe the structure of these Jordan blocks, which can be
encoded in certain directed graphs of Young diagrams, and show that they can
be read off from the so-called q,t-character of the representation.
Finally I discuss the connections of this result to some well-known integrable
systems with quantum affine sl(2) symmetry.
C. Zambon:
On generalized defects for the sine-Gordon model
Within the sine-Gordon model the possibility to have a fused pair of
integrable defects will be discussed. The interest for such an investigation
is twofold. On the one hand, it allows to define a new classical framework,
within which an integrable defect can be described that can be applied
successfully to a wider class of integrable field theories. On the other hand,
in the quantum context, special reductions of the transmission matrix describing
the scattering of a sine-Gordon soliton and a fused pair defects lead to the
soliton-soliton and lightest breather-soliton S-matrices, providing further
evidence that defects and solitons/breathers possess common features.