RAQIS 24

Slides

5. Bethe Ansatz for the Propagator of the Multi-Species Totally Exclusion Process.

Ali Zhara

We explore the dynamics of the N-species totally asymmetric simple exclusion process (N-TASEP) on a one-dimensional lattice, where different species of particles exhibit hierarchical dynamics depending on arbitrary parameters. We employ the Algebraic Bethe Ansatz method to establish a framework that enables the calculation of finite-time conditional probabilities for the positions of a finite...

3. Boundary energy of the quantum spin chain with various boundary terms.

Wen-Li Yang

Applying the recent developed method-the off-diagonal Bethe ansatz method, we construct the exact solutions of the Heisenberg spin chain with various boundary conditions. The results allow us to calculate the boundary energy of the system in the thermodynamic limit. The method used here can be generalized to study the thermodynamic properties and boundary energy of other high rank models with...

12. Coordinate Bethe Ansatz for N=2 SCFTs.

Juan Miguel Nieto García

In this talk I present a novel approach to the coordinate Bethe Ansatz which allowed the computation of the three-magnon wave function for the spin chains that capture the spectral problem of the marginally deformed Z2 orbifold of N=4 SYM in planar limit. The novel idea is to introduce contact terms that incorporate the dynamical structure of the spin chain.

20. Entanglement Hamiltonian for inhomogeneous free fermions.

Riccarda Bonsignori

The last two decades have witnessed an increasingly growing interest in the study and characterization of the entanglement structure of many-body quantum systems, also due to the development of related experiments. In this framework, a central object is the so-called entanglement Hamiltonian (EH), defined as the logarithm of the reduced density matrix, that provides a full description of the...

2. Exact dynamics with free fermions in disguise.

Istvan Vona

A large class of free fermionic spin chain models 2305.15625, 2310.19897, 2402.02984 have been found recently, that are not soluble by a Jordan-Wigner transformation, but by some more complex construction introduced in the original work 1901.08078 of Fendley, that rather resembles the methods to solve integrable systems. In 2405.20832 we relied on these techniques to calculate the correlation...

7. Exact loop densities in the O(1) dense loop model on an infinite cylinder of odd circumference.

Anastasiia Trofimova

Loop models are a class of two-dimensional statistical lattice models, and many classical models are equivalent to them. In this talk, we discuss the O(1) dense loop model on a square lattice wrapped on an infinite cylinder of odd circumference. Our main goal is to measure the average density of loops. We show that this problem is equivalent to finding the average density of percolation...

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

Tamas Gombor

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. 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...

10. F-bases, Bethe Ansatz, and Quantum Circuits.

Roberto Ruiz

We obtained a quantum circuit to prepare Bethe states. The quantum circuit is deterministic and has multi-qubit unitaries. The quantum circuit is limited to quantum-integrable spin-1/2 chains with periodic boundary conditions that are homogeneous nonetheless, such as the Heisenberg XXZ model. In this talk, we report our progress in the systematisation of quantum circuits for Bethe states. We...

9. From Set-Theoretical Solutions of the Braid Equation to Left Shelves.

Bernard Rybołowicz

In this talk, I will introduce the set-theoretic braid equation and the algebraic structure of a left shelf. I will demonstrate how to associate a solution with every left shelf and show that every left non-degenerate solution can be derived from a left shelf solution. Additionally, I will explore the equivalence of solutions under bijective maps, termed Drinfel’d isomorphisms. The...

18. Generalizations of spin Sutherland models from Hamiltonian reductions of Heisenberg doubles.

Laszlo Feher

We explain how Ruijsenaars--Schneider type deformations of two types of trigonometric spin Sutherland models arise from Hamiltonian reductions of Heisenberg doubles of compact semisimple Lie groups in general and from an extended Heisenberg double of the unitary group U(n) in particular. As of writing, the quantization of the resulting classical integrable systems is still an open problem.

14. Hybrid integrable systems.

Andrii Liashyk

We develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then we give several examples of hybrid integrable systems....

19. Integrability of the Inozemtsev spin chain and its generalization.

Oleg Chalykh

I will discuss a recent answer to an old open question regarding the integrability of the Inozemtsev spin chain. I will also explain how this quantum spin chain can be further generalised. Based on arXiv:2407.03276.

27. Integrable Quantum Field Theories, Irrelevant Perturbations and Minimal Form Factors.

Olalla Castro-Alvaredo

In this talk I will review some of my recent work on the form factor program for integrable quantum field theory in the presence of irrelevant perturbations. In particular, I will highlight how the solution to this problem can be employed to shed light on the structure of the form factors of more standard integrable quantum field theory, particularly their minimal form factors. I will consider...

6. Lagrangian multiforms: paths from classical to quantum.

Mats Vermeeren

Lagrangian multiform theory has appeared in the last 15 years as a variational approach to classical integrable systems. It describes both continuous and discrete systems, and initial steps have been made towards a quantum version. In this talk I will introduce Lagrangian multiform theory as it appears in classical integrable systems and its extensions to the semi-classical regime. I will...

15. Landscapes of integrable spin chains.

Rob Klabbers

Based on 2405.09718 with Jules Lamers: I discuss the general construction of integrable long-range spin chains from R-matrices, in particular the two known elliptic solutions to the sl2 Yang-Baxter equation. I'll show how each generates its own landscape of models, which connect only incidentally, and identify the various models that appear in each. In particular, I'll show how the...

11. Navier-Stokes equations for nearly integrable quantum gases.

Miłosz Panfil

The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this talk I will present recent results showing how the Navier-Stokes equations arise from the microscopic dynamics of nearly integrable 1d quantum many-body systems. The method builds upon the recently developed...

23. New integrable models: from short to long-range deformations.

Ana Retore

The integrability toolkit provides a powerful way to solve certain quantum models. It plays a role in several different areas of physics, being in particular responsible for remarkable progress in the context of AdS/CFT and statistical physics, and more recently in quantum circuits. Therefore, asking whether a model is integrable is a very relevant question, but not always an easy one. In this...

22. On correlation functions of the XXZ/XYZ open spin chain.

Véronique Terras

We review recent results concerning the computation of correlation functions in open XXZ and XYZ spin 1/2 chains with boundary fields. In the XXZ case with longitudinal boundary fields, correlation functions at zero temperature can be computed within the algebraic Bethe Ansatz framework in the form of multiple integrals in the half-infinite chain limit. We discuss the extension of this result...

8. On multipoint correlation functions in the Sinh-Gordon 1+1 dimensional quantum field theory.

Alex Simon

The S-matrix bootstrap program offers a unique possibility to compute explicitly the form factors of local operators in integrable quantum field theories. We shall build on those results so as to compute, in terms of explicit series of multiple integrals, the multipoint correlation functions in the Sinh-Gordon 1+1-dimensional quantum field theory, which is a simple case where the S-matrix is...

17. On the nested Bethe ansatz for a spin chain with simple Lie group symmetry.

Allan Gerrard

We present a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with g-symmetry for any simple Lie algebra g. Starting the nesting process by removing a single simple root from g, we use the residual U(1) charge and the block Gauss decomposition of the R-matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and...

24. On the recurrence relations for the Bethe vectors.

Stanislav Pakuliak

Different type recurrence relations for the off-shell Bethe vectors in the rational quantum integrable models are discussed. The off-shell Bethe vectors in the gl(N)- and o(2n+1)-invariant integrable models are considered. It is demonstrated that the recurrence relations for these Bethe vectors are based on the different hierarchical embedding of the smaller monodromy matrices into the bigger one.

4. Quantum many-body spin ratchets.

Lenart Zadnik

I will describe a novel class of exactly solvable quantum unitary circuits on qudits. Their key feature is architecture that breaks parity and time reversal symmetries, while retaining the combined PT symmetry. A consequence of this chirality is a spin transport with a finite drift: the circuit acts as a quantum spin pump. The drift velocity is universal in that it depends only on the Casimir...

21. Reflections on integrability.

Bart Vlaar

We will discuss recent developments and open problems in the algebraic theory of universal reflection equations and its application to quantum integrable systems with boundary conditions, which is one of its main motivations. The main class of examples is described by quantum symmetric pairs of affine type (a quantum affine algebra together with a so-called quantized fixed-point subalgebra)....

26. Set-theoretic YBE: quantum algebras & universal R matrices.

Anastasia Doikou

The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. We first introduce certain generalizations of the familiar shelves and racks called parametric (p)-shelves and racks. These objects satisfy a parametric self-distributivity condition and lead to solutions of the Yang-Baxter equation. Novel, non-reversible solutions are...

25. Solutions of tetrahedron and 3D reflection equations from quantum cluster algebras.

Atsuo Kuniba

Tetrahedron and 3D equations are three-dimensional generalizations of the Yang-Baxter and the reflection equations. I will explain how quantum cluster algebras lead to solutions that generalize and unify many known solutions.
Joint work with Rei Inoue, Xiaoyue Sun, Yuji Terashima and Junya Yagi.

13. Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type.

Maria Matushko

We discuss a matrix spin generalization of Ruijsenaars-Macdonald operators. We construct a commuting set of matrix-valued difference operators in terms of trigonometric GL(N|M)-valued R-matrices. Next, we present construction of long-range spin chains using the Polychronakos freezing trick. As a result, we obtain a new family of spin chains, which extends the gl(N|M)-invariant Haldane-Shastry...

1. Variational approach in quantum field theory.

Arthur Hutsalyuk

We develop a variational approach to study a two-dimensional non-integrable quantum field theories through the lenses of integrable ones. We focus on the φ4 Landau- Ginzburg theory and compare it with the integrable Sinh-Gordon. We employ exact Vacuum Expectation Values and Form Factors of local operators of the Sinh-Gordon model for getting the best variational estimates of several quantities...