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Related papers: On Bethe equations of 2d conformal field theory

200 papers

Three decades ago, Inozemtsev found an isotropic long-range spin chain with elliptic pair potential that interpolates between the Heisenberg and Haldane-Shastry (HS) spin chains while admitting an exact solution throughout, based on a…

Mathematical Physics · Physics 2022-05-17 Rob Klabbers , Jules Lamers

We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability…

Mathematical Physics · Physics 2025-03-27 Gwenaël Ferrando , Jules Lamers , Fedor Levkovich-Maslyuk , Didina Serban

This work inaugurates a series of complementary studies on Richardson-Gaudin integrable models. We begin by reviewing the foundations of classical and quantum integrability, recalling the algebraic Bethe ansatz solution of the Richardson…

High Energy Physics - Theory · Physics 2025-07-31 Grzegorz Biskowski , Franco Ferrari , Marcin R. Piatek

In this work, $\mathcal{PT}$-symmetric Hamiltonians defined on quantum $sl(2, \mathbb R)$ algebras are presented. We study the spectrum of a family of non-Hermitian Hamiltonians written in terms of the generators of the non-standard…

Quantum Physics · Physics 2023-09-28 Ángel Ballesteros , Romina Ramírez , Marta Reboiro

We show that, in the framework of covariant Hamiltonian field theory, a degenerate almost regular quadratic Lagrangian $L$ admits a complete set of non-degenerate Hamiltonian forms such that solutions of the corresponding Hamilton…

High Energy Physics - Theory · Physics 2009-10-31 L. Mangiarotti , G. Sardanashvily

The Levin-Wen string-net formalism provides a canonical mapping from spherical fusion categories to local Hamiltonians defining Topological Quantum Field Theories (TQFTs). While the topological invariance of the ground state is guaranteed…

High Energy Physics - Theory · Physics 2026-01-14 Hanshi Yang

The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted…

Quantum Algebra · Mathematics 2011-03-29 Alexander Varchenko

We study the ODE/IM correspondence for two-dimensional conformal field theories with Virasoro and $\mathcal{W}_N$ symmetry. Building on earlier work establishing the correspondence, we develop a systematic algorithm for calculating the…

High Energy Physics - Theory · Physics 2025-08-29 Matěj Kudrna , Tomáš Procházka

The Bethe ansatz equations of the fundamental Sp(2N) integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N-1 composite…

Statistical Mechanics · Physics 2016-08-31 M. J. Martins

It has been shown that the orbits of motion for a wide class of nonrelativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits…

Mathematical Physics · Physics 2011-05-12 Lawrence Horwitz , Avi Gershon , Marcelo Schiffer

We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…

Mathematical Physics · Physics 2009-08-03 M. J. Martins , C. S. Melo

In these notes we study integrable structures of conformal field theory with $\textrm{BCD}$ symmetry. We realise these integrable structures as affine Yangian $\mathfrak{gl}(1)$ "spin chains" with boundaries. We provide three solutions of…

High Energy Physics - Theory · Physics 2021-09-15 Alexey Litvinov , Ilya Vilkoviskiy

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The…

High Energy Physics - Theory · Physics 2023-07-18 Dmitry Chernyak , Azat M. Gainutdinov , Jesper Lykke Jacobsen , Hubert Saleur

We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the $sl_2$ loop algebra symmetry if the $q$ parameter is given by a root of unity, $q_0^{2N}=1$, for an…

Statistical Mechanics · Physics 2008-04-24 Tetsuo Deguchi

We establish a degeneration isomorphism between quantum toroidal algebras and untwisted affine Yangians, valid for all untwisted affine Kac-Moody Lie algebras. Specifically, we prove that the affine Yangian $Y_\hbar(\mathfrak{g})$ is…

Quantum Algebra · Mathematics 2026-05-14 Luan Bezerra , Iryna Kashuba , Hongda Lin

We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge…

High Energy Physics - Theory · Physics 2009-10-30 Boris Dubrovin , Youjin Zhang

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 K. E. Hibberd , C. Dunning , J. Links

Massless conformal scalar field in six dimensions corresponds to the minimal unitary representation (minrep) of the conformal group SO(6,2). This minrep admits a family of deformations labelled by the spin t of an SU(2)_T group, which is…

High Energy Physics - Theory · Physics 2015-06-18 Karan Govil , Murat Gunaydin

This is a review of recent developments in the theory of beta ensembles of random matrices and their relations with conformal filed theory (CFT). There are (almost) no new results here. This article can serve as a guide on appearances and…

Mathematical Physics · Physics 2014-08-19 Igor Rumanov

The quantum theory of the Liouville model with imaginary field is considered using the quantum inverse scattering method. An integrable structure with nontrivial spectral parameter dependence is developed for lattice Liouville theory by…

High Energy Physics - Theory · Physics 2009-10-28 L. D. FADDEEV , O. TIRKKONEN