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Related papers: Quantum toroidal gl(1) and Bethe ansatz

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In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 1/2 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice Sine-Gordon model…

High Energy Physics - Theory · Physics 2015-06-26 L. D. Faddeev

We prove a quantum version of the localization formula of Witten that relates invariants of a git quotient with the equivariant invariants of the action. Using the formula we prove a quantum version of an abelianization formula of S. Martin…

Symplectic Geometry · Mathematics 2016-08-10 Eduardo Gonzalez , Chris Woodward

We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by…

Mathematical Physics · Physics 2015-06-17 S. Pakuliak , E. Ragoucy , N. A. Slavnov

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…

High Energy Physics - Theory · Physics 2014-11-18 Luca Mezincescu , Rafael I. Nepomechie

We introduce a new class of generative quantum-neural-network-based models called Quantum Hamiltonian-Based Models (QHBMs). In doing so, we establish a paradigmatic approach for quantum-probabilistic hybrid variational learning, where we…

Quantum Physics · Physics 2019-10-07 Guillaume Verdon , Jacob Marks , Sasha Nanda , Stefan Leichenauer , Jack Hidary

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi

In this work we present a general construction of integrable models for boson tunneling in multi-well systems. We show how the models may be derived through the Quantum Inverse Scattering Method and solved by algebraic Bethe ansatz means.…

Mathematical Physics · Physics 2017-06-13 L H Ymai , A P Tonel , A Foerster , J Links

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a…

Mathematical Physics · Physics 2026-02-06 Xiaotian Xu , Wuxiao Wen , Tao Yang , Xin Zhang , Junpeng Cao

The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the off-diagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix…

Mathematical Physics · Physics 2015-06-19 Kun Hao , Junpeng Cao , Guang-Liang Li , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for describing tunneling phenomena of Bose-Einstein condensates. One of the significant mathematical properties of the model is that it can be exactly solved by Bethe ansatz…

Exactly Solvable and Integrable Systems · Physics 2008-04-24 Jon Links , Katrina E. Hibberd

We study solutions of the Bethe ansatz equation for the XXZ-type integrable model associated with the Lie algebra sl_N. We give a correspondence between solutions of the Bethe ansatz equations and collections of quasi-polynomials. This…

Quantum Algebra · Mathematics 2015-06-11 J. R. Li , V. Tarasov

We propose and develop the Bethe Ansatz method for the Heun equation. As an application, holomorphy of the perturbation for the BC_1 Inozemtsev model from the trigonometric model is proved.

Classical Analysis and ODEs · Mathematics 2009-11-07 Kouichi Takemura

We solve the XXZ Gaudin model with generic boundary using the modified algebraic Bethe ansatz. The diagonal and triangular cases have been recovered in this general framework. We show that the model for odd or even lengths has two different…

Mathematical Physics · Physics 2017-12-14 Nicolas Crampe

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations…

Mathematical Physics · Physics 2015-06-18 S. Pakuliak , E. Ragoucy , N. A. Slavnov

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial…

Mathematical Physics · Physics 2015-08-03 Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov

In the framework of the graded quantum inverse scattering method (QISM), we obtain the eigenvalues and eigenvectors of the supersymmetric $t-J$ model with reflecting boundary conditions in FFB background. The corresponding Bethe ansatz…

Condensed Matter · Physics 2009-10-31 Heng Fan , Bo-yu Hou , Kang-jie Shi

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are…

Mathematical Physics · Physics 2015-06-18 Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

In this paper we present two new numerical methods for studying thermodynamic quantities of integrable models. As an example of the effectiveness of these two approaches, results from numerical solutions of all sets of Bethe ansatz…

Strongly Correlated Electrons · Physics 2015-06-24 Shi-Jian Gu , N. M. R. Peres , You-Quan Li

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the…

Mathematical Physics · Physics 2013-10-08 Samuel Belliard , Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov