Titles and abstracts

Rouven Frassek

Baxter Perimeter Bethe Ansatz and Yangian invariants

I will discuss how Baxter's Perimeter Bethe Ansatz arises within the Quantum Inverse Scattering Method and the Algebraic Bethe Ansatz. We generalise the method to Baxter lattices with a boundary and discuss the relation to the boundary Yangian. Finally we sketch the relation to integrable boundary states. The talk is based on arXiv:1312.1693 and arXiv:1703.10842.

Extra material: https://rfrassek.github.io/web-export/index.html

Marius De Leew

Constrained Integrable Systems

In this talk I will discuss a systematic study of integrable models for spin chains with constrained Hilbert spaces. I will focus on spin-1/2 chains with the Rydberg constraint. I will classify all time-and space-reflection symmetric integrable Rydberg-constrained Hamiltonians of range 3 and 4. I will discuss a new model depending on a single coupling z and I will discuss some of its properties. We also perform a partial classification of integrable Hamiltonians for range 5.

Balàzs Pozsgay

TBA

Yupeng Yang

Exact surface energy of off-diagonal integrable models

With analysis of zero-roots of transfer mtrices, a systematic method will be introduced to compute physical quantities of quantum integrabe models without U(1) symmetry. 

Arthur Hutsalyuk

TBA

Chiara Paletta

Integrable open^2 quantum circuits 

Integrable unitary circuits can be seen as a Trotter formulation of some integrable continuous time Hamiltonian. Their importance lies in the potential to use analytical methods to compute physical observables, like correlation functions and mean particle current. In this talk, I will first explain the different parts of the title and how they are related: Integrability (Yang-Baxter integrability of a quantum model), Open (the word open is used in the context of open system: physical system in contact with an environment and open boundary conditions), Quantum circuits (discrete evolution of a physical system). In the second part, I will discuss some new results: I will build different quantum circuits by taking the elementary gate as the tensor product of two R-matrices of a spin ½ chain. By using Sklyanin's reflection algebra, I will address the question of which cases have the gate corresponding to the boundary matrix also factorized. This answer an old question on whether the integrability of the non-equilibrium state of a theory is related to the integrability of the full spectrum. Based on 2406.12695 with T. Prosen.

Simon Ekhammar

Q-functions, Functional SoV and Boundaries

Paul Ryan

Functional Separation of Variables & Correlation Functions

Fedor Levkovich-Maslyuk

Integrable Feynman Graphs and Yangian Symmetry on the Loom

We extend the powerful property of Yangian invariance to a new large class of conformally invariant Feynman integrals. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. We formulate Yangian symmetry in terms of a chain of Lax operators acting on the fixed coordinates around the graph, and we also extend this construction to the case of infinite-dimensional auxiliary space. Yangian invariance leads to new differential and integral equations for individual, highly nontrivial, Feynman graphs, and we present them explicitly for several examples. The graphs we consider determine correlators in the recently proposed loom fishnet CFTs. We also describe a generalization to the case with interaction vertices inside open faces of the diagram. Our construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs. Based on 2304.04654 and a paper to appear with V. Mishnyakov.

Wen-Li Yang

Eigenvalue relation of the Heisenberg chain with various boundary conditions for the ground state

We investigate the t − W scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation (the t − W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

Samuel Belliard

Modified Bethe ansatz

Tamas Gombor

Exact overlaps for integrable boundary states of gl(N) symmetric spin chains

In recent years, there has been growing interest (both in statistical physics and in the AdS/CFT duality) in exact overlaps between boundary and Bethe states. The off-shell overlaps are equivalent to certain partition functions of vertex models. Combining the algebraic Bethe Ansatz with the KT-relation (which is the defining equation of the integrable boundary states), a sum rule of off-shell overlaps can be derived. This sum rule is sufficient to express the on-shell overlaps in a determinant form. The results can be extended to the so-called integrable matrix product states. 

The talk would be based on the following papers:

arXiv:2110.07960

arXiv:2311.04870

and further unpublished results on matrix product states.

Davide Fioravanti

Exploring gauge theories and BHs with Floquet and Painlevé

We show how functional relations, which can be considered as a definition of a quantum integrable theory, entail an integral equation that can be extended upon introducing dynamical variables to a Marchenko-like equation. Then, we naturally derive from the latter a classical Lax pair problem. We exemplify our method by focusing on the massive/massless version of the ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence involving the sinh-Gordon/Lioville model, first emerged in the gauge theories and scattering amplitudes/Wilson loops AdS3 context with many moduli/masses, but in a way which reveals its generality. In fact, we give some hints, in the end, to its application to spin chains.

Miosz Panfil

Knot theory, lattice paths and partition functions of integrable models

In this talk I will explore physicist’s point of view on an old problem of classifying knots and relate it to a problem of counting certain lattice paths. The integrable spin models provide the bridge between the two areas. We will see that partition functions of these models take a universal form - can be encoded with a help of a special graph called quiver - and are related to the Donaldson-Thomas invariants. The language of integrable models leads also to a concept of 'quantization' of paths which can be independently seen from the topological recursion.

Jules Lamers

A solvable non-unitary fermionic long-range model with extended symmetry

Pascal Baseilhac

On the R-matrix presentation of the q−Onsager algebra

Martin Vrabec

q-Analogue of the degree zero part of a rational Cherednik algebra

The degree zero subalgebra of a rational Cherednik algebra (RCA) is interesting from the point of view of algebra, integrable systems, as well as geometry. This subalgebra is a flat deformation of the skew product of a finite Coxeter group with a quotient of the universal enveloping algebra of gl(n), and it is related to generalised Howe duality and to the theory of quantum Calogero-Moser systems.

Inside a double affine Hecke algebra, which depends on two parameters q and t, we define a subalgebra A that may be thought of as a q-deformation of the degree zero part of the corresponding RCA. We prove that the algebra A is a flat t-deformation of the skew product of a symmetric group with the image of the Drinfeld–Jimbo quantum group for gl(n) under the q-oscillator (Jordan-Schwinger) representation. We find all the defining relations and an explicit PBW basis for the algebra A. We describe its centre and establish a double centraliser property. Further, we develop the connection with certain quantum integrable systems of Macdonald-Ruijsenaars type introduced by van Diejen, which we also generalise. This talk is based on joint work with Misha Feigin.

Junpeng Cao

New quantum integrable models

Matthieu Cornillault

Partition function of the six-vertex model

Anastassia Trofimova