**CAUX Jean-Sébastien **
* Quench, Hydro and Floquet dynamics in integrable systems.*

pdf file of the presentation (13.5 Mo)

**DERRIDA Bernard **
* Renormalization and disorder: a simple toy model. *

The problem of the depinning transition of a line from a random substrate
is one of the simplest problems in the theory of disordered systems.
It has a long history among physicists and mathematicians.
Still there are many unsolved questions about the nature of this transition.
After a brief review of our present understanding of the problem,
I will discuss a simple toy model which indicates that the transition is
of infinite order of the Kosterlitz Touless type.

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**DE NARDIS Jacopo **
* Hydrodynamic diffusion in integrable systems from form-factors expansion.*

I will show how to compute the matrix of diffusion constants in integrable models
for generic stationary states by performing a spectral sum over intermediate states.
This is expressed as a sum over particle-hole excitations on top of a generic state with a
finite density of excitations (thermal or not). The result allows to compute diffusion constants and
to extend the hydrodynamic description of integrable models (usually denoted with
generalized hydrodynamics) to include terms of Navier-Stokes type which
lead to positive entropy production and diffusive relaxation mechanisms.

This work is in collaboration with D. Bernard and B. Doyon, arXiv:1807.02414.

pdf file of the presentation

**FRASSEK Rouven **
*Q-operators for rational spin chains.*

I plan to discuss how Q-operators for rational spin chains can be constructed in the
framework of the quantum inverse scattering method. The presentation will include open
and closed gl(n) type chains with compact and noncompact representations in the quantum
space. Also I plan to elaborate on the classification of the solutions relevant for
the Q-operator construction and their generalisations.

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**GAMAYUN Oleksandr **
* Integrable aspects of the mobile impurity.*

I consider an integrable model of a mobile impurity in 1D free fermions.
I present a full nonpertubative solution and express physical quantities in terms of
the Fredholm determinants of integrable integral operators. After a detailed
mathematical analysis of the obtained structures, I discuss several striking
physical phenomena such as incomplete relaxation and momentum dependent statistics.

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**GERRARD Allan **
* Nested Bethe ansatz for orthogonal and symplectic open spin chains.*

I will present the nested Bethe ansatz for open spin chains with so(2n) or sp(2n)
bulk symmetry and any diagonal boundary conditions. This talk will include an algebraic
description of this system, as well as some interesting properties of its nested Bethe
ansatz. Based on work with Vidas Regelskis and Curtis Wendlandt.

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**GIARDINÀ Cristian **
* An algebraic approach to stochastic duality.*

Duality is a key tool, of probabilistic nature,
in the analysis of several interacting particle systems.
Often a stochastic duality relation finds an explanation in
terms of an hidden symmetry of the process. This idea
was put forward by G. Schütz, who showed in 1997
that the duality of the asymmetric exclusion process
is due to the su_{q}(2) symmetry of the model.
I will discuss, by using a series of examples, how this
idea can be structured into a constructive algebraic
approach to duality theory of Markov processes.
In this context, representation theory of (quantum)
Lie algebras provides further insight in the understanding
of duality relations. If time allows, I will also present recent
developments relating stochastic duality and orthogonal
polynomials.

pdf file of the presentation

**GÖHMANN Frank **
* A form factor series for dynamical correlation functions of integrable
lattice models at finite temperature.*

We suggest a method for calculating dynamical correlation functions
at finite temperature in integrable lattice models of Yang-Baxter
type. The method is based on an expansion of the correlation functions
as a series over matrix elements of a time-dependent quantum transfer
matrix rather than the Hamiltonian. In the infinite Trotter-number
limit the matrix elements become time independent and turn into the
thermal form factors studied previously in the context of static
correlation functions. We make this explicit with the example
of the XXZ model. We show how the form factors can be summed
utilizing certain auxiliary functions solving finite sets of
nonlinear integral equations. The case of the XX model is worked
out in more detail leading to a novel form-factor series
representation of the dynamical transverse two-point function
that is promising for asymptotic analysis.

pdf file of the presentation

**HUTSALYUK Arthur **
*Algebraic Bethe ansatz multiple action formulas using current approach.*

Problem of calculation of scalar product and form factor in algebraic Bethe ansatz
requires to knowledge about actions of the monodromy matrix entries onto Bethe vectors.
Using current approach developed earlier by S.Z. Pakuliak et al. these multiple actions
can be derived in general case of SL(n|m) graded algebra.
Highest coefficients in the simplest case can be easy calculated.

pdf file of the presentation

**IMOTO Takashi **
*Exact regimes of collapsed and extra twostring solutions in the two down
spin sector of the spin 1/2 massive XXZ spin chain.*

We derive exactly the number of complex solutions with twodown spin in the massive
regime of the periodic spin 1/2 XXZ spin chain in N sites. Every solution of the
Bethe ansatz equations is characterized by a set of quantum numbers, which we call
the Bethe quantum numbers. We derive exactly them for all the complex solutions in the
sector, which we call two string solutions.
We show that in a region of N and Δ the number of two-string solutions is by
two larger than the number due to the string hypothesis, i.e., an extra pair of
two-strings appears.
We determine it exactly and also such regions where m two-string solutions collapse
for any positive integer m.

pdf file of the presentation

**JACOBSEN Jesper **
*Four-point functions in the Fortuin-Kasteleyn cluster model.*

The determination of four-point correlation functions of two-dimensional lattice
models is of fundamental importance in statistical physics. In the limit of an infinite
lattice, this question can be formulated in terms of conformal field theory (CFT). For
the so-called minimal models the problem was solved more than 30 years ago, by using
that the existence of singular states implies that the correlation functions must
satisfy certain differential equations. This settles the issue for models defined in
terms of local degrees of freedom, such as the Ising and 3-state Potts models. However,
for geometrical observables in the Fortuin-Kasteleyn cluster formulation of the Q-state
Potts model, for generic values of Q, there is in general no locality and no singular
states, and so the question remains open. As a warm-up to solving this problem, we
discuss which states propagate in the s-channel of such correlation functions, when
the four points are brought together two by two. To this end we combine CFT methods
with algebraic and numerical approaches to the lattice model.

pdf file of the presentation

**KOZLOWSKI Karol **
*Singularities of dynamic response functions in the massless regime of the XXZ chain.*

Dynamic response function correspond to space and time Fourier transforms of
dynamical two-point functions and are thus
functions of the momentum $k$ and energy ω.
Starting from the large-volume behaviour of the form factors of local operators
and building on certain hypotheses
relative to the existence of thermodynamic limits, I have constructed a series
of multiple integrals representing
the dynamic response functions in the massless regime of the spin-1/2 XXZ chain.

In this talk, I will describe a rigorous technique
allowing to analyse and fully describe the behaviour, in the (k,ω) plane, of
each multiple integral building up the mentioned series of multiple integrals.
In particular, the method unravels the presence of singularities in the (k,ω)
plane along certain curves ω=e(k).

This analysis confirms the predictions for the singular structure of the response
functions that were argued earlier
by means of a heuristic approach based on putting the model in correspondence
with a non-linear Luttinger Liquid.
It also stresses the importance of the role played by collective, equal velocity, excitations
on the generating mechanism of the singularity curves and the associated edge exponents.
Finally, this analysis sets a very simple picture allowing one to reduce the manifestation
of universal features characteristic of the Luttinger Liquid universality class to
the presence of certain
singularities in the large-volume behaviour of form factors of local operators and
to consequences of a classical asymptotic analysis of multiple integrals.

pdf file of the presentation

**LACROIX Sylvain **
*Quantum Affine Gaudin models.*

In this seminar, we will discuss results and conjectures about quantum affine Gaudin
models, concerning the construction of an infinite hierarchy of quantum commuting
Hamiltonians and their diagonalisation through the Bethe ansatz. Finally, we will
explore the possible relation of these results with the ODE/IM correspondence,
using the language of affine opers.

pdf file of the presentation

**LIASHYK Andrii **
*New determinant representations of scalar products in integrable models
associated to higher rank algebras.*

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz
and possessing gl(3)-invariant and gl(2|1)-invariant R-matrices. We study scalar
products of Bethe vectors of these models in the framework of Bethe ansatz. We give new
determinant representations for them.

pdf file of the presentation

**McCOY Barry **
*Deformation theory and Ising Correlations.*

In 1976 Wu, McCoy, Tracy and Barounch used the concept of
isomonodromic deformation to compute the scaling limit of the diagonal
correlation function of the Ising model in terms of the solution of a
Painlevé III equation. In 1981 Jimbo and Miwa applied isomonodromic
deformation theory to show that the diagonal correlation function
satisfies a Painlevé VI equation. It is therefore extremely natural to
extend this program to the correlation function for an arbitrary position
on the lattice. However, in the following 37 years this relation has not been
discovered. In this talk I will present the progress and the problems to be
solved in making this generalization.

pdf file of the presentation

**MORIN-DUCHESNE Alexi **
*Functional relations in the $A^{(1)}_2$ models.*

We investigate the family of $A^{(1)}_2$ statistical models. This family incorporates
a dilute loop model on the square lattice, the dimer model on the hexagonal lattice, `
the su(3) RSOS model and the $U_q(sl_3)$-invariant 15-vertex model.

We describe these models using the dilute Temperley-Lieb algebra, and construct
Wenzl-Jones projectors and fused face operators. The corresponding fused transfer
matrices satisfy sl(3)-type fusion hierarchies. We derive the corresponding T- and
Y-systems of functional equations. At roots of unity, we derive closure identities
for the functional relations.

pdf file of the presentation

**POZSGAY Balazs **
*Integrable states, exact overlaps, and the Boundary Yang-Baxter relation.*

We review the calculation of exact overlaps between Bethe states of spin chains
(including higher rank models) and certain integrable initial states. These include
two-site states and Matrix Product States (MPS), relevant for quenches and for AdS/CFT.
We show how the MPS can be obtained from No-scalar solutions to the (twisted) Boundary
Yang-Baxter relation, and also present new solutions.

pdf file of the presentation

**PRETI Michelangelo **
*Strongly deformed N=4 SYM in the double scaling limit as an integrable CFT.*

The Fishnet theory arises in the context of AdS/CFT correspondence as a strongly
deformed N=4 SYM and appear to be integrable in the spin chain formalism. We study that
theory in the double scaling limit of large imaginary twists and small coupling. We find
a closed expression for the 4point correlation function of the simplest protected
operators and use it to compute the exact conformal data.

pdf file of the presentation

**PROSEN Tomaž **
*Time-dependent matrix product ansatz for interacting reversible dynamics.*

We present an explicit time-dependent matrix product ansatz (tMPA) which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)]. Our construction is based on an explicit solution of real-space real-time inverse scattering problem. We consider two applications of this tMPA. Firstly, we provide the first exact and explicit computation of the dynamic structure factor in an interacting deterministic model, and secondly, we solve the extremal case of the inhomogeneous quench problem, where a semi-infinite lattice in the maximum entropy state is joined with an empty semi-infinite lattice. Both of these exact results rigorously demonstrate a coexistence of ballistic and diffusive transport behaviour in the model, as expected for normal fluids.

pdf file of the presentation

**ROUSSILLON Julien **
*Irregular conformal blocks and connection formulae for Painlevé V functions.*

We aim to present a CFT approach to Painlevé V equation. We show that irregular conformal
blocks of rank 1, for arbitrary central charge, are obtained as confluent limits of the
regular conformal blocks. Using this construction and the connection formulae for Painlevé
VI tau function, we obtain the connection coefficient between 0 and i∞ asymptotic
of Painlevé V tau function.

pdf file of the presentation

**SCHÜTZ Gunter **
*Duality and quantum algebra symmetry in stochastic particle systems.*

It is demonstrated how the quantum algebra symmetry of integrable quantum spin chains
gives rise to duality relations that allow for studying the microscopic structure and
dynamics of shock waves in stochastic interacting particle systems. The discussion
includes the large deviation regime of an untypically low current.

pdf file of the presentation

**SLAVNOV Nikita **
* Modified algebraic Bethe ansatz and scalar products.*

We study integrable models solvable by the modified algebraic Bethe ansatz (MABA).
Within the framework of this method, the original monodromy matrix is multiplied by a
generic (non-diagonal) twist matrix. This twist transformation leads to the change the
structure of the transfer matrix eigenvectors. We derive multiple action formulas on the
modified Bethe vectors. We also obtain a formula for the scalar product of generic
Bethe vectors. In the particular case of the off-shell-on-shell
scalar product, we find a compact determinant representation.

pdf file of the presentation

**SOTIRIADIS Spyros **
* Correlation functions of the quantum sine-Gordon model in and out of equilibrium.*

One of the main goals of QFT is the characterisation of a model through its correlation functions. In recent cold atom experiments it has become possible to directly measure multi-point correlation functions of the quantum sine-Gordon model, the theoretical calculation of which remains a challenging problem despite the integrability of the model. We present a numerical method for the computation of correlation functions of the sine-Gordon model, based on the Truncated Conformal Space Approach. We construct two and four point correlation functions in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We observe deviations from Gaussianity as measured by the kurtosis and analyse the dependence of the latter on interaction and temperature. Moreover we study dynamics after a quantum quench observing interaction effects on the spatiotemporal dependence of correlations.

pdf file of the presentation

**TERRAS Véronique **
*Integrable quantum spin chains by Separation of Variables: recent advances.*

We review the solution of different variants (closed or open, XXX/XXZ) of Heisenberg spin 1/2 chains by the quantum separation of variables approach. We notably discuss the computation of the scalar products of separate states (a family of states which generalizes the transfer matrix eigenstates) in the form of compact determinant representations.

pdf file of the presentation

**VANICAT Matthieu **
*Integrable Floquet dynamics, generalized exclusion processes and matrix ansatz.*

We present a general method for constructing integrable stochastic processes, with
twostep discrete time Floquet dynamics, from the transfer matrix formalism.
The models can be interpreted as a discrete time parallel update. The method can
be applied for both periodic or open boundary conditions. We also show how the
stationary distribution can be built as a matrix product state.

pdf file of the presentation

**VERNIER Eric **
*The rich symmetries of the U(1)-invariant Potts model.*

We will introduce a quantum chain generalizing the Potts model by keeping nearest-neighbour
interaction and self-duality, but further requiring U(1) invariance.
The latter connects in a simple way several ingredients found in the integrability
litterature, including the Onsager algebra, the chiral Potts model, and (quasi)local
charges associated to quantum groups at root of unity. We will explain the model's
degeneracies in terms of "n-strings", which can be thought of as ``non-quasi-particle''
excitations.
All this has interesting implications for the continuum limit conformal field theory,
which I will discuss if time allows.

pdf file of the presentation