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The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two…

Quantum Gases · Physics 2015-05-13 Guilhem Semerjian , Marco Tarzia , Francesco Zamponi

We introduce novel polynomial deformations of the Lie algebra $sl(2)$. We construct their finite-dimensional irreducible representations and the corresponding differential operator realizations. We apply our results to a class of spin…

Mathematical Physics · Physics 2025-09-16 Siyu Li , Ian Marquette , Yao-Zhong Zhang

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices…

High Energy Physics - Theory · Physics 2010-01-07 Yu-Kui Zhou

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two…

Mathematical Physics · Physics 2019-09-09 Samuel Belliard , Nikita A. Slavnov , Benoit Vallet

The one-dimensional small-polaron model with open boundary conditions is considered in the framework of the quantum inverse scattering method. The spin model which is equivalent to the small-polaron model is the Heisenberg $XXZ$ spin chain…

Condensed Matter · Physics 2007-05-23 Heng Fan , Xi-Wen Guan

We formulate a closed set of equations for the spectrum of two-dimensional bi-scalar fishnet conformal field theory, comprising Baxter equations and quantisation conditions, which we derive operatorially from the underlying sl(2) spin…

High Energy Physics - Theory · Physics 2026-04-03 Simon Ekhammar , Nikolay Gromov , Fedor Levkovich-Maslyuk , Paul Ryan

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting…

Statistical Mechanics · Physics 2020-04-21 Aleksandra A. Ziolkowska , Fabian H. L. Essler

We have considered the Zamolodchikov-Fateev and the Izergin-Korepin models with diagonal reflection boundaries. In each case the eigenspectrum of the transfer matrix is determined by application of the algebraic Bethe Ansatz.

Exactly Solvable and Integrable Systems · Physics 2010-04-07 V. Kurak , A. Lima-Santos

Solutions to the phonon Boltzmann transport equation under the relaxation-time approximation (RTA) are fundamentally limited in that they do not account for the off-diagonal elements of the scattering matrix, which encode intermode energy…

Computational Physics · Physics 2026-05-25 Y. Sungtaek Ju

The task of calculating operator dimensions in the planar limit of N=4 super Yang-Mills theory can be vastly simplified by mapping the dilatation generator to the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used in…

High Energy Physics - Theory · Physics 2012-08-27 Curtis G. Callan, , Jonathan Heckman , Tristan McLoughlin , Ian Swanson

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe…

Mathematical Physics · Physics 2015-07-02 C. Burdik , J. Fuksa , A. P. Isaev , S. O. Krivonos , O. Navratil

The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the graded osp(1|2) vertex model we find the…

solv-int · Physics 2009-10-31 A. Lima-Santos

We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables…

High Energy Physics - Theory · Physics 2025-12-19 Holger Frahm , Sascha Gehrmann , Rafael I. Nepomechie , Ana L. Retore

Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown…

Mathematical Physics · Physics 2014-05-15 J. F. van Diejen , E. Emsiz

We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…

Quantum Physics · Physics 2022-01-12 Pieter W. Claeys , Jonah Herzog-Arbeitman , Austen Lamacraft

To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper…

Mathematical Physics · Physics 2011-08-23 A. J. Macfarlane , H. Pfeiffer , F. Wagner

We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…

Computational Physics · Physics 2015-05-15 Jianfeng Lu , Christian B. Mendl

The generalized open XXZ model at $q$ root of unity is considered. We review how associated models, such as the $q$ harmonic oscillator, and the lattice sine-Gordon and Liouville models are obtained. Explicit expressions of the local…

High Energy Physics - Theory · Physics 2016-04-26 Anastasia Doikou

For generic values of q, all the eigenvectors of the transfer matrix of the U_q sl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is…

Mathematical Physics · Physics 2017-05-24 Azat M. Gainutdinov , Rafael I. Nepomechie

The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic…

Exactly Solvable and Integrable Systems · Physics 2008-03-12 G. von Gehlen , N. Iorgov , S. Pakuliak , V. Shadura