Related papers: Integrable systems, separation of variables and th…

Separation of variables (SoV) is a powerful method expected to be applicable for a wide range of quantum integrable systems, from models in condensed matter physics to gauge and string theories. Yet its full implementation for many higher…

We describe the extension, beyond fundamental representations of the Yang-Baxter algebra, of our new construction of separation of variables bases for quantum integrable lattice models. The key idea underlying our approach is to use the…

Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue…

Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of…

This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an…

Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently…

Using the framework of the quantum separation of variables (SoV) for higher rank quantum integrable lattice models [1], we introduce some foundations to go beyond the obtained complete transfer matrix spectrum description, and open the way…

We present a microscopic approach in the framework of Sklyanin's quantum separation of variables (SOV) for the exact solution of 1+1-dimensional quantum field theories by integrable lattice regularizations. Sklyanin's SOV is the natural…

Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…

We apply our new approach of quantum Separation of Variables (SoV) to the complete characterization of the transfer matrix spectrum of quantum integrable lattice models associated to gl(n)-invariant R-matrices in the fundamental…

We implement our new Separation of Variables (SoV) approach for open quantum integrable models associated to higher rank representations of the reflection algebras. We construct the (SoV) basis for the fundamental representations of the…

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated…

The analysis of the transfer matrices associated to the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method which generalizes…

We derive an integral expression for the leading-order type I-I-I three-point functions in the $\mathfrak{su}(2) $-sector of $\mathcal{N}=4$ super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the…

In this paper we consider the spin 1/2 highest weight representations for the 6-vertex Yang-Baxter algebra on a finite lattice and analyze the integrable quantum models associated to the antiperiodic transfer matrix. For these models, which…

The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV)…

We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a…

In [1], the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This…

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference…