Out-of-equilibrium phases of matter have triggered a lot of attention in the last decade, since new and interesting physical phenomena with no equilibrium counter parts can arise. The 1d interacting Bose-gas for example possesses bound states for attractive interactions but is experimentally highly unstable at equilibrium. However, these bound states become stable out-of-equilibrium since the...

We study the ground state one-body correlation function in the Lieb-Liniger model. In the spectral representation, correlations are built from contributions stemming from different excited states of the model. We aim to understand which excited states carry significant contributions, specifically focusing on the small energy-momentum part of the dynamic one-body function. We conjecture that...

In this talk I provide an overview on the appearance of integrability - especially in the form of Yangian symmetry - in the context of several different quantities in four-dimensional quantum field theories. In particular, I discuss how superconformal Yangian symmetry shows up in different forms in the context of planar N=4 super-Yang-Mills (SYM) theory, whose spectral problem famously maps...

Scattering processes in integrable theories are traditionally associated with particle number conservation. This is indeed the case for asymptotic states, yet at intermediate time-scales decaying excitations are allowed. The family of homogeneous sine-Gordon (HSG) models provides a rare example of an integrable quantum field theory where both stable and unstable bound states are present in the...

Quantum lattice nonlinear Schroedinger equation will be explained: history, open problems and applications [including nuclear physics].

In this talk, I will talk about the holographic description of the osp(1|2) super conformal blocks on the sphere and the torus. I will concentrate on the 2-point and 3-point conformal blocks on the sphere and the 1-point and 2-point blocks on the torus. I will present some results we have obtained in a work in process (to be published soon). It is known that the holomorphic part of primary...

In this talk, I will show a new connection we found between quantum integrable models and black holes perturbation theory. After a brief introduction to quasinormal modes and their role in gravitational waves observations, I will connect their mathematically precise definition with the integrability structures derived from the differential equation associated to the black hole perturbation....

The inhomogeneous six-vertex model is a multi-parametric integrable 2D statistical system. With the anisotropy parameter |q|=1, the model is critical and is expected to exhibit a variety of interesting universal behaviour. In this talk we discuss the scaling limit of the homogeneous and so-called staggered cases and mention some applications to QFT. We also describe a conjecture from...

The finite-size spectrum of the critical alternating Z2-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is presented. For all values of the staggering parameter the continuum limit has been found to be described in terms of the non-compact SU(2, R)/U(1) Euclidean black hole conformal field theory (CFT) whose scaling dimensions include a continuous component. In...

The totally asymmetric exclusion process (TASEP) is a continuous time Markov process much studied in statistical physics featuring particle with hard-core interaction hopping randomly on a one dimensional lattice.

This talk will focus on the study of the fluctuations of the particle current in the TASEP with open boundaries in the thermodynamic limit. More precisely, the eigenvalues of a...

Exclusion processes in one dimension first appeared in the 70's and have since dragged much attention from communities in different domains: stochastic processes, out of equilibriums statistical physics and more recently integrable systems. While it is well known that the hydrodynamic limit of the single species totally asymmetric simple exclusion process (TASEP) is described by the Burger's...

We will discuss models on discrete 1+1 dimensional space-time, which display different versions of solvability. The models include both classical and quantum mechanical systems. The two main mechanisms underlying solvability are the traditional forms of integrability, and the more recent idea of dual unitarity. We will explore these ideas and survey a number of different integrable models.

We discuss anomalous fluctuations recently observed in the (anisotropic) Landau-Lifhsitz model in equilibrium, a paradigmatic integrable model of interacting classical spins. Typical fluctuations of the time-integrated spin current on sub-ballistic scales are non-Gaussian and the cumulants are found to grow with different (algebraic) exponents, unlike in the "standard" scenario of the theory...

In integrable models when an operator couples to a conserved charge its decay will be algebraic along rays in spacetime due to few-body scattering processes giving rise to 'sound waves' ballistically propagating. There are example of operators that do not produce these waves but still encode fundamental information. Remarkable examples are the so called twist fields, present whenever there is...

The staircase model is an integrable modification of the sinh-Gordon model, obtained by complexifying the coupling constant. A key feature of this theory is the fact that the scaling function displays a roaming behaviour, that is, it visits all the unitary minimal conformal models when varying the temperature.

Via the generalized hydrodynamics (GHD) approach to iQFT, we develop a more...

The one dimensional δ-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra cold atoms in one dimensional traps. Even though the model is integrable, integrability breaking effects are always present in the real world experiments. In this work we consider the integrability breaking due to atomic loss, which is the most relevant...

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum...

Integrable models are special quantum many-body systems because they posses a large number of conserved charges, which enables one to treat these models with analytic tools. However, in usual integrable systems (e.g. XXZ model) certain computations - for example the calculation of correlation functions - are very difficult to tackle exactly. Therefore in recent years ,,simpler'' integrable...

I will discuss a class of very simple integrable dynamics on a discrete space-time lattice, which is generated by a 2-site matrix-valued rational map.

The phase spaces of the matrix variable can be selected from diverse families of symmetric spaces, e.g. complex Grassmannians, and are equipped with a natural symplectic structure.

This precise form of the map follows from a simple...

The bipartite fidelity was introduced in 2011 by Stéphan and Dubail as an entanglement measure in quantum many-body systems. It is expressed in terms of the overlap between the groundstate of the whole system and a tensor product of groundstates for two complementary subsystems. For one-dimensional quantum critical systems, the bipartite fidelity has an interpretation in terms of conformal...

The eigenvalues of the quantum transfer matrix (QTM) of the XXZ spin-1/2 chain in the Trotter limit are parameterized by solutions of non-linear integral equations (NLIEs). We analyze these equations in the low-temperature limit for the model in the antiferromagnetic massless regime at finite magnetic field. To leading order in T the solutions of the NLIEs are determined by the dressed energy,...

In this talk, I will describe our investigations of the universal behaviour of two critical percolation models: site percolation on the triangular lattice and bond percolation on the square lattice. Both are Yang-Baxter integrable models that can in principle be solved exactly. In the scaling limit, they are conformally invariant and described by non-unitary representations of the Virasoro...

The presence of a global internal symmetry in a quantum many-body system is reflected in

the fact that the entanglement between its subparts is endowed with an internal structure, namely

it can be decomposed as sum of contributions associated to each symmetry sector. The study of

the symmetry resolution of entanglement measures provides a formidable tool to probe the outof-

equilibrium...

In this talk the excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory in 1+1D with an internal U(1) symmetry will be studied. It will be shown both for bosons and fermions theories that the ratio of charged moments between the excited and ground states take a extremely simple and universal form depending...

One class of exactly solvable quantum many-body systems is the set of dual unitary quantum circuits, whose fundamental quantum gate is also unitary in the space direction. In these models the infinite temperature dynamical correlation functions can be calculated exactly both for integrable and chaotic systems. For local dimension N=2 the complete classification is known, and multiple general...

Local measurements can sometimes lead to unexpected macroscopic behaviours. Such “measurement catastrophes” in integrable models go beyond generalized hydrodynamics, that is arguably the most effective large-scale description of dynamics in integrable models in the presence of inhomogeneities. A noteworthy occurrence of this phenomenon is found in systems exhibiting quantum jamming. I will...

On this talk we'll review the basic concepts of non-linear sigma models and in

particular the one-parameter integrable deformation of the 2d O(3) sigma model.

We'll explore the solutions of this system via thermodynamic bethe ansatz, Y-systems and Dynkin TBA and how to apply this techniques on a Field theory as the one we are dealing with here.

In the second part of this presentation...