The hydrodynamic approximation is an extremely powerful tool to describe the behaviour of many-body systems such as gases. At the Euler scale, the approximation is based on the idea of local entropy maximisation: locally, within fluid cells, the system relaxes to a state that takes the Gibbs form. In conventional gases, these are thermal states, which include the few conserved quantities...
In two-dimensional critical loop models, including the O(n) and Potts models, the spectrum is exactly known, as are a few structure constants or ratios thereof. In this talk, I will propose an exact formula for arbitrary four-point structure constants. The formula is a function of conformal dimensions, built from Barnes' double Gamma function, times a polynomial function of loop weights. Using...
The idea that ferromagnetic transitions correspond to the percolation of clusters of like spins has been present since the early days of the theory of critical phenomena. It turned out, however, that its implementation requires trading the obvious spin clusters for a more sophisticated version known as Fortuin-Kasteleyn clusters. It has been conjectured for long time that in the...
We consider a spin chain corresponding to an open quantum system described by the Lindblad equation, where the external driving acts in the bulk. This model corresponds to a new integrable range 3 elliptic deformation of Hubbard. We show the appearance of multiple NESS: the system retains memory of the initial state, even though the obvious symmetries of the Hamiltonian are broken. We motivate...
The notion of a Manin triple of Lie algebras arises in many contexts in quantum integrable systems and beyond. After recalling the general definition, I will describe one important class of examples involving current algebras, i.e. certain Lie algebras associated to the punctured formal disc in complex dimension one. Studying these examples naturally leads one to recover the ideas of vertex...
Quantum Gaudin models were introduced in 1976 to study integrable spin chains with long-range interactions. Since then, they have found many applications in modern mathematical physics.
The integrable structure of Gaudin models of finite type is very well understood, i.e., there is a precise description of the commutative subalgebra of the conserved charges, and their spectrum can be...
I discuss the oscillator construction for Q-operators of rational spin chains in the closed and open setting. Some focus will be given on the closed case of type BCD and the orthosymplectic case osp(N|2m).
We build the quasiparticle picture for the tripartite mutual information (TMI) after quantum quenches in spin chains that can be mapped onto free-fermion theories. A nonzero TMI (equivalently, topological entropy) signals quantum correlations between three regions of a quantum many-body system. The TMI is sensitive to entangled multiplets of more than two quasiparticles, i.e., beyond the...
Integrability equips models of theoretical physics with efficient methods for the exact construction of useful states and their evolution. Relevant tools for classical integrable field models in one spatial dimensional are spectral curves in the case of periodic fields and inverse scattering for asymptotic boundary conditions. Even though the two methods are quite different in many ways, they...
We consider the effects of so-called Frustrated Boundary Conditions (FBC) on quantum spin chains, namely periodic BC with an odd number of sites. In absence of external fields, FBC allow for the direct determination of correlation functions that signal a spontaneous symmetry breaking, such as the spontaneous magnetization. When paired with anti-ferromagnetic interactions, FBC introduce...
I will describe recent progress in the understanding and construction of Q-operators for open quantum spin chains. The construction exploits the the universal K-matrix picture of Appel and Vlaar. The resulting open Q-operator and the functional relations it obeys follow by pure representation theory; this opens the route to broad generalisation.
We present a physical interpretation and mathematical evidence for the modular transforms of GGEs that was discussed in arXiv:2111.13950. We presented a conjecture for the modular transform of the partition function of a simple GGE in a single free fermion model as a curious product over three apparently independent sets of fermion modes. We have now generalised the result to GGEs composed of...
Scattering amplitudes in gravitational theories provide useful tools for the calculation of observables associated to encounters of compact objects, such as black holes and neutron stars. In this talk, I will discuss recent progress in exploring the classical limit of scattering amplitudes and their connection to gravitational observables in $\mathcal{N}=8$ supergravity, which serves as a...
Global symmetries of quantum many-body systems can be spontaneously broken. Whenever this mechanism happens, the ground state is degenerate and one encounters an ordered phase. In this study, our objective is to investigate this phenomenon by examining the entanglement asymmetry of a specific region.
We explicitly demonstrate our construction in the ordered phase of the Ising field theory in...
I will summarise some of the results obtained in two recent papers (with O. Castro-Alvaredo and S. Negro) where we developed a form factor program for TTbar-perturbed integrable quantum field theories. In particular, I will show how useful information about the physics behind this particular kind of deformation can be extracted from the form factor expansion of correlation functions. This...
A big challenge of modern-day many-body theory is to expand the existing (mostly equilibrium) toolbox to treat out-of-equilibrium problems, for example quantum quenches. Results are predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution; such overlaps are unavailable in most cases. For integrable models, as often...
If we start from certain functional relations as definition of a quantum integrable theory, then we can derive from them a linear integral equation. It can be extended, by introducing dynamical variables, to become an equation with the form of Marchenko's. Then, we derive from the latter a classical (differential) Lax pair. We exemplify our method by focusing on the massive version of the...
In this talk, I will explain how to apply some integrability tools like QQ-system , TQ-relation or Thermodynamic Bethe Ansatz to some 4D N=2 gauge theories and realistic black holes models. In fact, those theories mathematically are completely characterised by some shared Ordinary Differential Equation (ODE) which we study through the celebrated ODE/IM correspondence with 2D Integrable Models...
We review the ODE/IM correspondence for higher-order ODEs associated with affine Toda field equations. We focus on the exact WKB periods and the TBA equations for higher-order ODEs and their wall-crossing phenomena, which describe a rich structure of the ODE/IM correspondence. We also discuss its supersymmetric extension and application to quantum mechanics with effective potential.
Due to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution, or its Fourier transform known as full counting statistics (FCS), contains much more information than say the mean value of the measured observable and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the...
We introduce a new elliptic quantum toroidal algebra $U_{q,t,p}(\mathfrak{gl}_{1,tor})$ and show some interesting representations including the level (0,0) representation given by the elliptic Ruijsenaars difference operators. We also construct intertwining operators of the $U_{q,t,p}(\mathfrak{gl}_{1,tor})$-modules w.r.t. the Drinfeld comultiplication and give a realization of the affine...
The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped 1D systems. Despite this fact, its complete thermodynamic description in all its regimes was lacking. In the talk, I will report the filling of this gap by deriving the Thermodynamic Bethe Ansatz framework that captures the thermodynamics of the model and serves as the...
The sine-Gordon model is an integrable field theory that captures the effective dynamics of a wealth of one-dimensional quantum systems, and thus is of central interest for a broad community. A convenient experimental platform consists of two tunnel-coupled onedimensional quasicondensates: the great tunability of this setup makes it a convenient quantum simulator of the field theory, realizing...
$\mathcal{N}=4$ Super Yang-Mills Theory in 4 dimensions is a Super-conformal Gauge Theory known to be integrable in the planar limit. In the past decade its full finite size spectrum was solved by the Quantum Spectral Curve (QSC) method. Structure Constants for asymptotically large operators were computed at finite t'Hooft coupling by the integrability based Hexagonalization approach. However...
Understanding the non-equilibrium dynamics of many-body quantum systems is a notoriously hard task due to the exponential increase of the Hilbert space dimension with the number of the system’s components. This prevented, for a long time, a direct comparison between theory and the available experimental measures with ultracold atoms and ions. In recent years, the advent of Generalized...
An infinite number of evolution equations dictate the dynamics of quantum integrable models according to generalized hydrodynamics (GHD). At the Euler scale in the T=0 limit, with a single Fermi sea, GHD is known to become equivalent to conventional Euler hydrodynamics. The T=0 GHD, also known as zero entropy GHD, describes integrable models with the splitting of Fermi seas, which has no...
Spectrum of planar N=4 super Yang-Mills theory (SYM) is known to be exactly solvable from integrability, in principle. In practice, only a handful of states were solved non-perturbatively. We introduce a new integrability-based numerical tool called the Fast Quantum Spectral Curve (QSC) Solver, and using it, we solve the spectral problem for N = 4 SYM fully, systematically, efficiently and...
We are defining and studying a fermionic integrable model which is a long-range version of the XXZ model at $\Delta=0$. The model can be obtained as the q=i limit of the q-deformed Haldane-Shastry model studied previously. Unlike its short-distance cousin, and very much like the Haldan-Shastry model, it possesses extended symmetry. The model is non-unitary and has unusual properties. In the...
One of the most attractive features of supersymmetric gauge theories is a striking cross-fertilization of distinct exact techniques, like integrability, bootstrap, and supersymmetric localization. In recent years, certain integrated correlators emerged as a natural incarnation of that interplay, leading to a new tool to probe the non-perturbative regime of those models. In this talk, I will...
I discuss several aspects related to the edge behavior of 2d integer quantum Hall droplets of arbitrary shapes, and its relation to two-dimensional Coulomb gases at a specific inverse temperature.
Both systems can be mapped onto free fermions, with single particle wave functions which can be determined exactly in the limit of large particle number. It is well known that the two problems can...
We propose a new family of non-integrable spin-1 chains with exactly solvable subspace. Based on the idea of the tower of quasiparticle excitations, a series of non-integrable Hamiltonians with exactly solvable subspace and the associated exactly solvable energy eigenstates is constructed. The obtained exactly solvable energy eigenstates are the candidates of quantum many-body scar states,...
We consider the four-vertex model with a particular choice of fixed boundary conditions, closely related to scalar products of off-shell Bethe states. In the scaling limit, the model exhibits the limit shape phenomenon, with the emergence of an arctic curve separating a central disordered region from six frozen ‘corners’ of ferroelectric or anti-ferroelectric type. We determine the analytic...
We consider 1/2 BPS supersymmetric circular Wilson loops in $\mathcal{N}=2$ $SU(N)$ SYM theories with massless matter content and non-vanishing $\beta$-function. In flat space we compute the observable via perturbative techniques, employing dimensional reduction to regularize the ultraviolet divergences and performing standard renormalization. We extend the analysis on the sphere...
The exact characterization of order parameter correlations in the presence of strongly fluctuating interfaces is a notoriously difficult problem in classical statistical mechanics. In this talk we present exact results for order parameter and energy density correlations for an interface forming a droplet in two dimensions whose endpoints are pinned on a wall. Our framework, which hinges on...
We study a family of higher-twist Regge trajectories in $\mathcal{N}=4$ supersymmetric Yang-Mills theory using the Quantum Spectral Curve. We explore the many-sheeted Riemann surface and show the interplay between the higher-twist trajectories and the several degenerate non-local operators, called (near-)horizontal trajectories, that have a strong connection to light ray operators, objects...
The entanglement asymmetry quantifies how much a given state is far from being invariant under a certain group. If studied in the ground state of a system, it quantifies how much the system breaks (either explicitly or spontaneously) a given symmetry group. Formulated in the modern language, symmetries of a QFT are implemented by topological defects and, accordingly, the entanglement asymmetry...
In this talk I will discuss how the framework of exact WKB analysis underlies a definition of instanton partition functions beyond weak coupling regimes. In the context of four-dimensional theories with extended supersymmetry exact computations of partition functions are made possible by localization techniques. On the one hand localization hinges on the existence of a Lagrangian...
