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Related papers: Algebraic Bethe Ansatz for XYZ Gaudin model

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We derive a criterion under which splitting of all eigenstates of an open $\XYZ$ Hamiltonian with boundary fields into two invariant subspaces, spanned by chiral shock states, occurs. The splitting is governed by an integer number, which…

Statistical Mechanics · Physics 2022-09-14 Xin Zhang , Andreas Klümper , Vladislav Popkov

We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalised inhomogeneous five-vertex model on the square lattice, given certain conditions hold,…

Combinatorics · Mathematics 2007-05-23 R. Brak , J. W. Essam , A. L. Owczarek

We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to…

Mathematical Physics · Physics 2017-06-28 Rouven Frassek

In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin-$\frac12$ chain on the segment with two generic integrable boundaries acting on the Bethe vector. The essential step is to prove…

Mathematical Physics · Physics 2015-10-05 J. Avan , S. Belliard , N. Grosjean , R. A. Pimenta

The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe…

Statistical Mechanics · Physics 2017-08-16 Frank Göhmann , Alexander Seel

In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to…

Exactly Solvable and Integrable Systems · Physics 2011-02-16 A. Lima-Santos

In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain…

Statistical Mechanics · Physics 2022-07-29 Marius de Leeuw , Chiara Paletta

Interacting matter-radiation models close to physical systems are proposed, which without rotating wave approximation and with matter-matter interactions are Bethe ansatz solvable. This integrable system is constructed from the elliptic…

Statistical Mechanics · Physics 2016-08-31 Anjan Kundu

We study the Izergin-Korepin Gaudin models with both periodic and open integrable boundary conditions, which describe quantum systems exhibiting novel long-range interactions. Using the Bethe ansatz approach, we derive the eigenvalues of…

Mathematical Physics · Physics 2025-06-12 Xiaotian Xu , Pei Sun , Xin Zhang , Junpeng Cao , Tao Yang

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using…

Mathematical Physics · Physics 2018-04-27 Antonio Lima-Santos , Rafael I. Nepomechie , Rodrigo A. Pimenta

The boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented. The eigenvalues…

Exactly Solvable and Integrable Systems · Physics 2019-08-21 R. S. Vieira , A. Lima Santos

We consider the gl_N Gaudin model of a tensor power of the standard vector representation. The geometric Langlands correspondence in the Gaudin model relates the Bethe algebra of the commuting Gaudin Hamiltonians and the algebra of…

Quantum Algebra · Mathematics 2009-07-21 E. Mukhin , V. Tarasov , A. Varchenko

We study solutions of the Bethe Ansatz equation related to the trigonometric Gaudin model associated to a simple Lie algebra g and a tensor product of irreducible finite-dimensional representations. Having one solution, we describe a…

Quantum Algebra · Mathematics 2009-04-06 E Mukhin , A Varchenko

A new form of Bethe ansatz equations is introduced. A version of a separation of variables for the quantum $sl_3$ Gaudin model is presented.

Quantum Algebra · Mathematics 2007-05-23 E. Mukhin , V. Schechtman , V. Tarasov , A. Varchenko

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…

Mathematical Physics · Physics 2011-02-16 Daniel Arnaudon , Nicolas Crampe , Anastasia Doikou , Luc Frappat , Eric Ragoucy

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…

High Energy Physics - Theory · Physics 2009-08-03 W. Galleas

Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver (VQE) approach to estimating Bethe roots of…

Quantum Physics · Physics 2025-01-28 David Raveh , Rafael I. Nepomechie

The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the numbers of real self-dual spaces in intersections of Schubert…

Quantum Algebra · Mathematics 2018-05-17 Kang Lu

We derive a number of results related to the Gaudin model associated to the simple Lie algebra of type G$_2$. We compute explicit formulas for solutions of the Bethe ansatz equations associated to the tensor product of an arbitrary…

Quantum Algebra · Mathematics 2025-04-15 Kang Lu , E. Mukhin

Let $M$ be a tensor product of unitarizable irreducible highest weight modules over the Lie (super)algebra $\mathcal{G}$, where $\mathcal{G}$ is $\mathfrak{gl}(m|n)$, $\mathfrak{osp}(2m|2n)$ or $\mathfrak{spo}(2m|2n)$. We show, using super…

Mathematical Physics · Physics 2024-02-08 Wan Keng Cheong , Ngau Lam