AVAN Jean
Quantization of trace-brackets
The quantization problem for the trace-bracket algebra, derived from
double Poisson brackets, is discussed. We obtain a generalization of the
boundary YBE for the quantization of the quadratic trace-brackets. A
dynamical deformation is proposed on the lines of Gervais-Neveu-Felder
quantum algebras.
BATCHELOR Murray
Integrability vs exact solvability in the quantum
Rabi model and beyond
The quantum Rabi model, which describes the simplest interaction between
light and matter, is a fundamental model with widespread applicability in
quantum physics. The applications include the interaction between light
and trapped ions or quantum dots, and between microwaves and
superconducting qubits. The model is also applicable to both cavity and
circuit QED. The eigenspectrum of the quantum Rabi model has recently been
obtained exactly and the model has been claimed to be integrable. This
talk will discuss recent work with Huan-Qiang Zhou on examining the
Yang-Baxter integrability of this model. In particular, it is found that
the quantum Rabi model does not appear to be Yang-Baxter integrable in
general. It is however, integrable in two special limits. These
considerations can be extended to various physical generalisations of the
Rabi model.
BELLIARD Samuel
Modified algebraic Bethe ansatz.
We present a modified version of the algebraic Bethe ansatz (MABA) that
allows to characterize the eigenvalues and the eigenstates of spin chains
without U(1) symmetry [Belliard Crampé (2013)] and work in progress. The
XXX and XXZ Heisenberg spin chains on the segment will be discussed. The
solution involves the Baxter T-Q equation with an inhomogeneous term
introduced by [Cao et al. (2013)] and used in the quantum separation of
variable approach by [Niccoli et al. (2014)]. The MABA also produces the
associated Bethe vectors.
BOROT Gaetan
Asymptotic expansion in 1d log-gas with many-body interactions
1d log-gas are systems of N particles on the real line, subjected to a Coulomb repulsion in 2d, and possibly to other non-singular interactions. Their appear in random matrix theory, in Chern-Simons theory, in statistical physics on the 2d random lattice, ... I will give an overview of systematic methods based on large deviations and Schwinger-Dyson equations to obtain large N asymptotic expansion in such models, and give some examples of applications in integrable and non-integrable models.
This talk is based on joint works with Alice Guionnet and Karol Kozlowski.
BROCKMANN Michael
Gaudin-like determinants for overlaps in
integrable models and their applications to quench problems
We study interaction quenches defined by releasing the ground state of a
non-interacting theory into a system with finite interaction. We focus
here on the spin-1/2 Heisenberg chain and the Lieb-Liniger Bose gas.
Starting from exact overlaps between the initial state and Bethe
eigenstates we show that an application of the quench action method allows
to give an exact description of the post-quench steady state in the
thermodynamic limit. This steady state in particular correctly reproduces
expectation values of local correlators.
CANTINI Luigi
Inhomogenous Multi-TASEP (M-TASEP) on a ring with spectral parameters
I will report on some ongoing work about a multispecies version of the
TASEP, a model which describes the stochastic evolution of a system of
particles of different species (labeled by an integer) on a periodic
oriented one dimensional lattice, where two neighboring particles exchange
their position with a rate which depends on their species. For some choice
of these rates the Markov matrix turns out to be integrable and for the
same choice the (unnormalized) stationary probability is conjectured to
show remarkable positivity and combinatorial properties. By introducing
spectral parameters in the problem we will uncover a novel algebraic
structure underlying this problem which will allow us to provide exact
formulas for the stationary probability of some configurations.
CAUDRELIER Vincent
Set-theoretical reflection equation in integrable
field theories and fully discrete systems
The Yang-Baxter equation (YBE) is central in the theory of integrable systems. It has been mainly studied and used in the quantum realm. But it was suggested by Drinfeld in 1990 that the general study of the so-called Ç set-theoretical YBE È is also important. It turns out that the dressing method in the theory of classical integrable field theories provides a means to construct solutions to this equation, called Yang-Baxter maps, by looking at soliton collisions. Using the vector nonlinear Schršdinger (NLS) equation as the main example, we will review this notion of "classical solutions of the quantum YBE". Then, we will show how the new concept of set-theoretical reflection equation naturally emerges by studying the vector NLS on the half-line. The study of soliton collisions on the half-line provides solutions to this equation, called reflection maps. It is the beauty of integrable systems that completely classical and nonlinear field theories share common fundamental structures with their quantum counterparts. Such notions have direct applications to discrete integrable systems and raise the question of the general geometric picture in the context of Poisson-Lie groups.
CAUX Jean-Sébastien
Exact solutions for quenches in the Lieb-Liniger
Bose gas and Heisenberg quantum spin chains
A number of recent results on the out-of-equilibrium dynamics of
integrable models will be presented, based on a novel method for
explicitly calculating the relaxation of observables following a quantum
quench. Specifically, interaction quenches in the Lieb-Liniger model will
be treated, as well as anisotropy quenches in quantum spin chains.
DEGUCHI Tetsuo
Formulas of form factors for the spin-1/2 and
integrable spin-s XXZ chains and non-equilibrium dynamics
We derive various expressions of the form factors for the spin-1/2 XXZ
chain and the integrable spin-s XXZ chains, which are useful for studying
the non-equilibrium dynamics of the integrable quantum many-body systems.
We first show compact formulas for the form factors of arbitrary operators
in the spin-1/2 XXZ chain and those of the integrable higher-spin XXZ
chains. The compact formulas have several applications: One can evaluate
the reduced density matrices systematically through them; One can also
derive the multiple-integral representations of arbitrary correlation
functions at zero temperature for the integrable higher-spin XXZ chains
[1,2]. Furthermore, we transform the compact formulas into those which can
be evaluated through the Fredholm determinants. We show that they are
numerically and practically useful. For instance, we show the time
evolution of physical operators such as the local magnetization in the XXZ
spin chain through them.
[1] T. Deguchi and C. Matsui, Nucl. Phys. B831[FS] (2010) 359;
[2] T. Deguchi, JSTAT (2012) P04001.
DELFINO Gesualdo
Universal results for two-dimensional percolation
We present recent universal results for percolation in two
dimensions obtained using conformal and integrable
quantum field theory. At criticality we point out a
connection with time-like Liouville field theory and obtain the
three-point connectivity constant. Away from
criticality we determine the universal amplitude
ratios as well as the asymptotic crossing probabilities. Our results
are confirmed by high precision numerical simulations.
DIAF Ahmed
Bound state solutions of D-dimensional Feynman propagator with the
Wood-Saxon potential
An analytical expression for the energy eigenvalues of the Wood-Saxon
potential for l-states, based on the path integral formalism, is derived
by an approximation to the centrifugal term of the potential, in the
framework of the Duru-Keinert method. Nonlinear space-time transformations
in the radial path integral are applied. A transformation formula is
derived that relates the original path integral to the Green function of a
new quantum soluble system. The energy spectrum and the normalized
eigenfunctions are both obtained for the application of this technique to
the Wood-Saxon potential. Our results are in very good agreement with
those found using other approximation methods.
DUGAVE Maxime
Thermal form factors of the anisotropic Heisenberg chain
We derive expressions for the form factors of the quantum transfer matrix of the spin?1/2 XXZ chain which are suitable for taking the infinite Trotter number limit.
These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model.
We consider form factor expansions of the longitudinal and transversal two-point functions.
Remarkably, the formulae for the amplitudes are in both cases of the same form.
The usefulness of our novel formulae is demonstrated by working out explicit results in the low-temperature limit in the massless regime at finite magnetic field.
By summing up the most relevant terms in the form factor series, we obtain the low-temperature large-distance asymptotics of the two-point functions, which is in accordance with conformal field theory predictions.
Moreover, we obtain explicit expressions for the amplitudes which can be efficiently evaluated numerically.
Finally, we present recent results for the massive regime at zero temperature.
EVANS Martin
The Asymmetric Exclusion Process: an exactly solvable nonequilibrium
system
The asymmetric exclusion process models the stochastic transport of a
conserved quantity (mass, cars, molecular motors etc) through an open
system. Since a current of mass always flows, the system is out of
equilibrium but will nevertheless attain a nonequilibrium stationary state
in the long time limit. In this talk I will give an overview of how the
stationary state can be solved exactly by a matrix product ansatz
resulting in a quadratic algebra. I will discuss the phase diagram and
additional dynamical transitions. I shall also discuss generalisations to
multispecies system resulting in higher rank tensor product states and
richer algebraic relations.
FADDEEV Ludwig D
Zero modes for the Liouville model
I propose to use for the definition of zero modes in the quantum Liouville
Model the canonical variables, entering the monodromy matrix of the
corresponding Lax operator. introduced . This matrix was investigated by
Takhtajan and me in the middle of 80-ties and was one of the sources for
quantum groups amd their role in CFT.
FALDELLA Simone
Spin chains by separation of variables method
TBA
FEHER Laszlo Recent
developments in the reduction approach to action-angle dualities of
integrable many-body systems
Key properties of integrable Hamiltonian systems can be often viewed as
consequences of their realizations as reductions of "canonical free
systems" having rich symmetries on higher dimensional phase spaces. We
first summarize results of the last few years towards explaining known
action-angle duality relations between one-dimensional classical
integrable many-body systems in terms of Hamiltonian reduction. We then
present our recent results such as for example the construction of new
self-dual compact forms of the trigonometric Ruijsenaars-Schneider system
and the description of a novel dual pair involving the trigonometric BC(n)
Sutherland system.
FOERSTER Angela
Integrability in ultracold physics
The impressive development in cooling and trapping atoms in 1D tubes
brought the area of integrable systems to a new audience, when it became
clear that these models can be realized in the lab. Prominent examples
include the Lieb- Liniger model for spinless bosons and the Gaudin-Yang
model for two-component fermions. In this work we give an overview of
these ongoing developments. In addition, new results, such as the Wilson
ratio of the 1D attractive Fermi gas with spin imbalance [1] and a
geometric ansatz for a few particles system [2] will be presented. Finally
we discuss how the breakdown of integrability in the fundamental 1D model
of bosons with contact interactions affects the stationary correlation
properties of the system [3]. In principle, all these results can be
detected by state-of-the art experiments.
[1] X. W. Guan, X. G. Yin, A. Foerster, M. T. Batchelor, C. H. Lee, H. Q.
Lin, Phys. Rev. Lett. 111 (2013) 130401.
[2] B. Wilson, A. Foerster, C. C. N. Kuhn, I. Roditi, D. Rubeni, Phys.
Lett. A 378 (2014) 1065.
[3] I. Brouzos and A. Foerster, Broken Integrability Trace on Stationary
Correlation Properties, arXiv:1405.0430, to appear in PRA.
GAINUTDINOV Azat
The periodic sl(2|1) alternating spin chain and
Logarithmic Conformal Field Theory at c = 0
Abstract TBA
GOEHMANN Frank
Form factor approach to correlation functions of
the XXZ chain for delta larger than one
Abstract TBA
GOLDSTEIN Garry
GGE and applications for integrable systems
We study the nonequilibrium properties of 1-D interacting systems. For the
1-D Lieb Liniger gas we introduce a new version of the Yudson
representation applicable to finite size systems. We provide a formalism
to compute various correlation functions for highly nonequilibrium initial
states. In the strong coupling regime we are able to find explicit
expressions for the density, density-density and related correlation
functions. We are able to show that for initial sates with smooth
correlations the gas equilibrates at long times. For nearly translationaly
invariant states the gas equilibrates to the GGE. We show that for other
integrable models, ones with bound states, the GGE fails. We also apply
our results on equilibration and the GGE to studying initial states with
small Yang-Yang entropies in the Tonks Girardeau regime. We show that at
long time such states have universal power law density-density
correlations.
GOMES Jose Francisco
Backlund Transformation for mKdV Hierarchy
A systematic construction of Integrable hierarchies is proposed in
terms of an Affine Kac-Moody algebra. In particular we
shall discuss the mKdV hierarchy and its higher
nonlinear solitonic equations. We explicitly construct the
Backlund transformation for the mKdV equation as well
as for the first few higher members of the hierarchy
KAROWSKI Michael
O(N) Bethe Ansatz and exact form factors of the
O(N) sigma and Gross-Neveu models
General form factor formulas for the O(N) and Gross-Neveu models are
constructed and applied to several operators. The large N limits of these
form factors are computed and compared with the 1/N expansion of the
models in terms of Feynman graphs and full agreement is found. In
particular for the O(3)-model several low particle form factors are
calculated explicitly.
KHARLAMOV Mikhail
Some integrable systems with algebraic separation
of variables
We consider integrable systems of mechanical origin with a compact
configuration space. Such a system is called irreducible if it does not
have any continuous symmetry group and therefore does not reduce,
globally, to a family of systems with two degrees of freedom. One of the
known examples of an irreducible system was found by A.G. Reyman and M.A.
Semenov-Tian-Shansky [1]. It is a widest of known generalizations of the
classical Kowalevski case and the Kowalevski--Yehia gyrostat [2]. The
integrable systems with two degrees of freedom appear in an irreducible
system as invariant almost symplectic submanifolds of dimension 4. They
are called critical subsystems. First, we present the complete
classification of critical subsystems for the system found in [1]. If the
gyrostatic momentum in this problem is zero, there exist exactly three
critical subsystems. For two of them we present an algebraic separation of
variables, i.e., two auxiliary variables satisfy the equations of the
Kowalevski type and all initial phase variables are expressed in terms of
the separated ones as rational functions of simple radicals with
polynomial coefficients. One separation is integrated in elliptic
functions, another is hyperelliptic. Considering the phase space of the
separated variables as a 4-dimensional Euclidean space of two coordinates
and two momenta, we derive the polynomial equations for the Hamilton
function H. In the elliptic case it is of degree 4 with respect to H. The
work is partially supported by the RFBF (research project No.
14-01-00119).
[1] A.G. Reyman, M.A. Semenov-Tian-Shansky. Lax representation with a
spectral parameter for the Kowalewski top and its generalizations. Lett.
Math. Phys. 14, 1987, 55-61.
[2] H.M. Yehia. New integrable cases in the dynamics of rigid bodies.
Mech. Res. Commun. 13, 1986, 169-172.
KLUEMPER Andreas
Non-linear integral equation approach to sl(2|1)
integrable network models
Abstract TBA
KONNO Hitoshi
Elliptic Quantum Groups, Drinfeld Coproduct and Deformation of
W-algebras
We first discuss a quantum Z-algebra structure of the elliptic algebra Uq,p(g)
associated with an untwisted affine Lie algebra g, and show that the
irreducibility of the level-k representation of the Uq,p(g)-module
is governed by the corresponding Z-algebra module. The level-1 examples
for g=Al(1), Bl(1), Dl(1)
show that the irreducible Uq,p(g)-modules are decomposed as a
direct sum of the irreducible W-algebra modules. We secondly introduce the
Drinfeld coproduct to Uq,p(g) and discuss the intertwining
operators (vertex operators) with respect to this new coproduct.
Constructing the vertex operators for the level-1 Uq,p(g)-modules
with g=Al(1), Bl(1), Dl(1)
explicitely, we show that the these vertex operators factor the generating
functions of the known deformed W-algebras associated with Al(1),
Dl(1), and further obtain a conjectural expression
for the Bl(1) case corresponding to a deformation of
Fateev-Lukyanov's WBl-algebra.
KORFF Christian
Solving the Bethe ansatz equations: generalised quantum Schubert calculus
One of the main obstacles in obtaining the exact solution of exactly solvable lattice models is solving the Bethe ansatz equations. This problem is usually considered to be intractable. In this talk I will focus on two 5-vertex degenerations of the asymmetric six-vertex model and present the solution for arbitrary anisotropy parameter $\Delta$. By using a special parametrisation of the Boltzmann weights, the problem of solving the equations reduces to the explicit description of a coordinate ring (a polynomial algebra modulo certain relations). For special values of the anisotropy parameter this ring has been of great interest in the mathematics literature. At the free fermion point $\Delta=0$ one obtains the quantum cohomology and at the combinatorial point $\Delta=1/2$ the quantum K-theory of Grassmannians. Both objects appear in the context of the study of moduli spaces of curves and have their origins in CFT and string theory. The combinatorics which describes the multiplication in these rings is known as quantum Schubert calculus. Our work allows us to use the six-vertex model to define a generalised complex oriented cohomology for the Grassmann varieties and use it to explicitly compute K-theoretic Gromov-Witten invariants.
This is joint work with Vassily Gorbounov, Aberdeen.
KOSTOV Ivan
Quasiclassical expansion of the Slavnov determinant
We propose a systematic way to compute the quasi-classical expansion of
the on-shell/off-shell scalar product of multi-magnon states in the
generalised SU(2) model. We give explicit expressions for the first two
terms of the expansion in terms of contour integrals.
LOEBBERT Florian
Spin Chains and Three-Point Functions in N=4 SYM
Theory
We propose a new method for the computation of quantum three-point
functions for operators in su(2) sectors of N=4 super Yang-Mills theory.
The method is based on the existence of a unitary transformation relating
inhomogeneous and long-range spin chains. This transformation can be
traced back to a combination of boost operators and an inhomogeneous
version of Baxter's corner transfer matrix. We reproduce the existing
results for the one-loop structure constants in a simplified form and
indicate how to use the method at higher loop orders. Then we evaluate the
one-loop structure constants in the quasiclassical limit and compare them
with the recent strong coupling computation.
MAHMOOD Irfan
Non-commutative and Quantum Painlevé II equation
My poster will consist the non-vacuum solitonic solutions of the
non-commutative Painleve II equation with the help of its Darboux
transformation for which the solution of Toda equations at n = 1 and its
negative counter part has been taken as a seed solution. Further it will
involve the construction of Darboux transformations for Toda solutions
that are applied to express non-commutative PII solutions explicitly
interns of quasideterminants of Toda solutions. Further, I derive a zero
curvature representation of quantum Painleve II equation and its Riccati
form which can be reduced to the classical Painleve II when h → 0.
MATVEEV Vladimir
From continous to the discrete Fourier transform: classical and quantum aspects
We explain and generalize certain results by Mehta relating the eigenfunctions of quantum harmonic oscillator with the eigenvectors of the discrete Fourier transform (DFT). Using far more general construction based on a kind of Poisson summation, we associate the eigenvectors of the DFT with the sums of any absolutely convergent series. This construction in particular provides the overcomplete bases of the DFT eigenvectors by means of Jacobian theta functions or ? theta-functions and leads, in a quite natural way to some new identities and addition theorems in the theory of special and q-special functions
MAILLET Jean-Michel
Form factor approach to correlation functions
in massless quantum integrable models
Abstract TBA
NEPOMECHIE Rafael
On the completeness of solutions of Bethe's
equations
Ever since Bethe solved the spin-1/2 Heisenberg model, the nagging
question of completeness has persisted: namely, whether the Bethe
equations (BE) have too many, too few, or just the right number of
solutions to account for all the eigenstates of the Hamiltonian. We shall
argue that, in some sense, there are too many: the BE have many "singular"
solutions, of which only a small subset (the "physical singular"
solutions) correspond to eigenstates of the Hamiltonian. We find a
condition for identifying the physical singular solutions. We formulate a
conjecture for the number of solutions of the BE with pairwise distinct
roots, in terms of numbers of singular solutions. Using homotopy
continuation methods, we find all such solutions of the BE for chains of
length up to 14, and observe perfect agreement with the conjecture. We
briefly discuss the generalization to higher spin.
NICCOLI Giuliano
SOV approach for the exact solution of integrable
quantum models: the open XXZ spin chain
Abstract TBA
NIJHOFF Frank
Lagrangian Multiform Theory and Integrability
Recent developments in the theory of discrete integrable systems, in
particular the notion of multidimensional consistency and its
consequences, has led to the formulation of a novel variational principle
based on the notion of Lagrangian multiforms, introduced by Lobb and
Nijhoff in 2009. The talk reviews the main ideas and recent results,
including the quantum aspects.
PALMAI Tamas
Quench echo and work statistics in integrable quantum field theories
We study integrable quantum field theories in the context of out of
equilibrium situations, in particular from a thermodynamic point of view.
Such studies so far have only been carried out for non-interacting models
and those equivalent to such. To take into account genuine interactions we
develop a boundary thermodynamic Bethe ansatz technique for the
computation of the statistics of the work done when a global quench is
performed in the elementary mass scale. We find analytic expressions for
the low energy part of the statistics and we also present numerical
results for the simplest relativistic integrable QFT, the sinh-Gordon
model, where we study in particular the effects of turning on the
interaction relative to the case of the free boson theory.
PASQUIER Vincent
On Bethe Ansatz for the open XXX chain
Abstract TBA
PEARCE Paul Exact
solution of critical dense polymers with Robin boundary conditions
Solvable critical dense polymers is a loop model on the square lattice
with central charge c=-2 and loop fugacity β=0 so that closed loops are
forbidden. We solve this model exactly on a strip with general Robin
boundary conditions which are given as a linear combination of Neumann and
Dirichlet boundary conditions on the loops allowing loops to terminate on
the boundary. We classify the eigenvalues of the double row transfer
matrices using the physical combinatorics of the patterns of zeros in the
complex spectral parameter plane and obtain finitized characters related
to spaces of coinvariants of Z4 fermions. In the continuum
scaling limit, the Robin boundary conditions are associated with
irreducible Virasoro Verma modules with conformal weights given by a Kac
table with half-integer Kac labels: Δr,s-1/2=(L2-4)/32
where L=2s-1-4r, r∈ Z, s∈ N.
PIMENTA Rodrigo
Algebraic Bethe ansatz for 19-vertex models with
upper triangular K-matrices
By means of an algebraic Bethe ansatz approach we study the
Zamolodchikov-Fateev and Izergin-Korepin vertex models with non-diagonal
boundaries, characterized by reflection matrices with an upper triangular
form. Generalized Bethe vectors are used to diagonalize the associated
transfer matrix. The eigenvalues as well as the Bethe equations are
presented.
REGELSKIS Vidas
Twisted Yangians for symmetric pairs of types B,
C, D
I will present a class of quantized enveloping algebras, called twisted
Yangians, associated with the symmetric pairs of types B, C, D in terms of
the Cartan classification of compact Riemannian symmetric spaces. These
algebras play an important role in quantum integrable systems with open
boundary conditions. They are regarded as coideal subalgebras of the
extended Yangian for orthogonal or symplectic Lie algebras, whose defining
relations are written in an R-matrix form. On the other hand, these
algebras can be presented as quotients of the reflection equation algebra
by additional symmetry relations.
RUIJSENAARS Simon
A recursive construction of joint eigenfunctions
for the commuting hyperbolic Calogero-Moser Hamiltonians
We present a recursive scheme involving so-called kernel functions, which
yields an explicit diagonalization of the hyperbolic N-particle
Calogero-Moser quantum systems of nonrelativistic and relativistic type.
For the nonrelativistic case, the first step of the scheme yields the
well-known 2-particle eigenfunction, basically a specialization of the
Gauss hypergeometric function. The work on the N>2 case (together with
Martin HallnŠs) gives rise to an elementary representation of the joint
eigenfunctions, which were previously obtained in a quite different form
by Heckman and Opdam. Last but not least, we sketch a similar recursive
construction for the joint eigenfunctions of the 2N commuting relativistic
hyperbolic Calogero-Moser Hamiltonians.
RYABOV Pavel
Phase topology of generalized two-field gyrostat
We consider the integrable system with three degrees of freedom for which
Sokolov and Tsiganov specified a Lax representation. This representation
generalizes the L--A pair of the Kowalevski gyrostat in two constant
fields found by Reyman and Semenov-Tian-Shansky. We give explicit formulas
for two almost everywhere independent additional first integrals K and G.
These integrals are functionally connected with the coefficients of the
spectral curve of the L--A pair by Sokolov and Tsiganov. In the talk, we
suggest an approach to describe phase topology of a new integrable system
with three degrees of freedom, using the method of critical subsystems.
The notion of a critical subsystem was formed in the beginning of 2000-ies
in the problem of study of phase topology of irreducible systems with
three degrees of freedom. Due to the obtained form of additional integrals
K, G and parametric reduction, we managed to find analytically invariant
four-dimensional submanifolds on which the induced dynamic system is
almost everywhere Hamiltonian with two degrees of freedom. The system of
equations that describes one of these invariant submanifolds is a
generalization of the invariant relations of the corresponding integrable
Bogoyavlensky case for the rotation of a magnetized rigid body with a
fixed point in homogeneous magnetic and gravitational fields. For each
subsystem, we construct the bifurcation diagrams and specify the
bifurcations of Liouville tori both in subsystems, and in the system as a
whole. We also present new net diagrams on isoenergetic surfaces
(analogues of Fomenko's nets), which are not in the list of net invariants
in the problem of the Kowalevski top motion in the case of a double force
field. The work is partially supported by RFBR, research project No.
14-01-00119.
SEMENOV-TIAN-CHANSKI Michel
Difference Lax operators, Poisson Lie groups and
differential/difference Galois theory
I discuss the lift of the Poisson structure in the space of
differential/difference Lax operators to the space of solutions of the
associated auxiliary linear problem (the space of wave functions). The key
phenomenon is a peculiar symmetry breaking which makes the associated
differential/difference Galois group a Poisson group. I shall describe a
new class of classical r-matrices associated with generalized
exchange-algebras. Reduction to the case of higher order scalar difference
Lax operators is particularly rigid; in this case all Poisson structures
are defined in a unique way.
SLAVNOV Nikita
Form factors in quantum integrable models with
Gl(3)-invariant R-matrix
We consider form factors of the monodromy matrix entries in quantum
integrable models with Gl(3)-invariant R-matrix and find detreminant
representations for them. We show that all determinant representations are
related with each other by a set transformations in such a way, that it is
enough to find the determinant formula for only form factors. All others
follow from this initial representation.
SUZUKI Junji
Correlations in massive phase
The quantum correlation functions of spin chains in massive phase will be
addressed. (Joint work with M. Dugave, K. Kozlowski and F. Goehmann)
VLJIM Rogier
Applications of algebraic Bethe ansatz matrix elements to spin chains
Algebraic Bethe ansatz based techniques at finite size afford a way into computing observables for integrable models. Dealing with Bethe roots explicitly as deviated string-solutions is necessary. Dynamical correlations of the Babujan-Tahktajan spin-1 chain are obtained by a higher spin generalisation of this method. The obtained real-space spinÐspin correlation displays asymptotics fitting predictions from conformal field theory. Moreover, prepared out-of-equilibrium initial states for the anisotropic spin chain can be addressed as well. For the Néel state in particular as an initial state, contributions from coinciding deviated strings at zero are challenging to implement.
WANG Yupeng The
inhomogeneous T-Q relation and solutions of integrable models without
reference state
The off-diagonal Bethe ansatz method will be introduced. By constructing
the operator product identities, the inhomogeneous T-Q relation can be
constructed. This method overcomes the difficulty of the absence of a
reference state for models without U(1) symmetry. Applications of this
method on several models will be introduced.
YANG Wen-Li
Off-diagonal Bethe ansatz for the Izergin-Korepin model with
non-diagonal boundary terms
The Izergin-Korepin model with general non-diagonal boundary terms, a
typical integrable model beyond A-type and without U(1)-symmetry, is
studied via the off-diagonal Bethe ansatz method. Based on some intrinsic
properties of the R-matrix and the K-matrices, certain operator product
identities of the transfer matrix are obtained at some special points of
the spectral parameter. These identities and the asymptotic behaviors of
the transfer matrix together allow us to construct the inhomogeneous T-Q
relation and the associated Bethe ansatz equations. In the diagonal
boundary limit, the reduced results coincide exactly with those obtained
via other methods.
ZULLO Federico
Backlund transformations and a q-difference Baxter's equation for the
Ablowitz-Ladik chain.
We shall give the Baxter's operator and the corresponding Baxter's
equation for a quantum version of the Ablowitz Ladik model. The result is
achieved in two different ways: by using the well-known Bethe ansatz
technique and looking at the quantum analogue of the classical Backlund
transformations. General results about integrable models governed by the
same r-matrix algebra will be given. The Baxter's equation comes out to be
a q-difference equation involving both the trace and the quantum
determinant of the monodromy matrix. We will show how the spectrality
property of the classical Backlund transformations gives a trace formula
representing the classical analogue of the Baxter's equation. Finally we
will discuss a q-integral representation of the Baxter's operator.