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We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the…

High Energy Physics - Theory · Physics 2011-02-16 Olivier Babelon , Dmitri Talalaev

A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables…

Exactly Solvable and Integrable Systems · Physics 2017-03-10 Maxim Nazarov , Evgeny Sklyanin

Using the nested coordinate Bethe ansatz, we study 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they…

Mathematical Physics · Physics 2017-05-03 N. Crampe , L. Frappat , E. Ragoucy , M. Vanicat

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version…

Exactly Solvable and Integrable Systems · Physics 2016-12-28 R. C. T. Ghiotto , A. L. Malvezzi

The Nested Bethe Ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex models and…

High Energy Physics - Theory · Physics 2009-10-28 H. J. de Vega , A. González--Ruiz

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell…

Mathematical Physics · Physics 2016-10-04 Rafael I. Nepomechie , Rodrigo A. Pimenta

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…

Mathematical Physics · Physics 2016-08-18 Lijun Yang , Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…

Statistical Mechanics · Physics 2009-10-31 Gunter M. Schütz

We propose a set of conventional Bethe Ansatz equations and a corresponding expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms, provided that the boundary…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

We study the tensor product of the {\it higher spin representations} (see the definition in Sect. 2.2) of the elliptic quantum group $E_{\tau,\eta}(sl_n)$. The transfer matrices associated with the $E_{\tau,\eta}(sl_n)$-module are exactly…

High Energy Physics - Theory · Physics 2010-04-05 Bo-yu Hou , Ryu Sasaki , Wen-Li Yang

Exact quantum integrability is established for a class of multi-chain electron models with correlated hopping and spin models with interchain interactions, by constructing the related Lax operators and R-matrices through twisting and gauge…

Condensed Matter · Physics 2009-11-07 Anjan Kundu

The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The…

Mathematical Physics · Physics 2015-01-19 Samuel Belliard

Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…

Quantum Physics · Physics 2016-06-29 Naila Amir , Shahid Iqbal

We consider the feasibility of studying the anisotropic Heisenberg quantum spin chain with the Variational Quantum Eigensolver (VQE) algorithm, by treating Bethe states as variational states, and Bethe roots as variational parameters. For…

Quantum Physics · Physics 2021-01-26 Rafael I. Nepomechie

This paper is a review of the works devoted to understanding and reinterpretation of the theory of quantum integrable models solvable by Bethe ansatz in terms of the theory of purely classical soliton equations. Remarkably, studying…

Mathematical Physics · Physics 2025-03-19 A. Zabrodin

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

We investigate Bethe Ansatz equations for the one-dimensional spin-$\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case…

Condensed Matter · Physics 2007-05-23 Shao-shiung Lin , Shi-shyr Roan

We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The…

High Energy Physics - Theory · Physics 2021-09-01 Rafael I. Nepomechie , Ana L. Retore

In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains.…

High Energy Physics - Theory · Physics 2015-06-17 A. Gorsky , A. Zabrodin , A. Zotov

The exact solution of an integrable anisotropic Heisenberg spin chain with nearest-neighbour, next-nearest-neighbour and scalar chirality couplings is studied, where the boundary condition is the antiperiodic one. The detailed construction…

Mathematical Physics · Physics 2020-06-03 Yi Qiao , Jian Wang , Junpeng Cao , Wen-Li Yang