RAQIS'18: Titles and abstracts

Compressed folder (.tar.gz) of all presentations (40 Mo)

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.
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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 suq(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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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