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The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of…

Statistical Mechanics · Physics 2009-11-10 F. C. Alcaraz , M. J. Lazo

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

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where…

Quantum Physics · Physics 2017-02-09 Feng Pan , Yao-Zhong Zhang , Jerry P. Draayer

The lattice spin model with $Q$--component discrete spin variables restricted to have orientations orthogonal to the faces of $Q$-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The…

Statistical Mechanics · Physics 2015-06-25 V. R. Ohanyan , L. N. Ananikyan , N. S. Ananikian

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s…

High Energy Physics - Theory · Physics 2009-11-10 H. Dimov , R. C. Rashkov

The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld…

Statistical Mechanics · Physics 2011-04-22 C. W. Campbell , K. A. Dancer , P. S. Isaac , J. Links

In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only…

Mesoscale and Nanoscale Physics · Physics 2013-05-30 Omar El Araby , Vladimir Gritsev , Alexandre Faribault

We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin…

High Energy Physics - Theory · Physics 2015-04-10 Pulak Ranjan Giri , Tetsuo Deguchi

A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model…

Statistical Mechanics · Physics 2009-11-13 Diana Antonosyan , Stefano Bellucci , Vadim Ohanyan

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…

High Energy Physics - Theory · Physics 2009-10-31 V. Fridkin , Yu. Stroganov , D. Zagier

We derive exactly the number of complex solutions with two down-spins in the massive regime of the periodic spin-1/2 XXZ spin chain of $N$ sites. Here we remark that every solution of the Bethe ansatz equations is characterized by a set of…

Statistical Mechanics · Physics 2019-05-22 Takashi Imoto , Jun Sato , Tetsuo Deguchi

Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…

Exactly Solvable and Integrable Systems · Physics 2026-01-01 Jon Links

We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary…

Statistical Mechanics · Physics 2019-09-18 Enej Ilievski , Eoin Quinn

Bethe ansatz equations for spin-$s$ Heisenberg spin chain with $s\ge1$ are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra…

High Energy Physics - Theory · Physics 2024-05-01 Jue Hou , Yunfeng Jiang , Rui-Dong Zhu

We construct Drinfel'd twists for the rational sl(n) XXX-model giving rise to a completely symmetric representation of the monodromy matrix. We obtain a polarization free representation of the pseudoparticle creation operators figuring in…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 T. -D. Albert , H. Boos , R. Flume , K. Ruhlig

We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…

High Energy Physics - Theory · Physics 2021-05-19 Zoltán Bajnok , Etienne Granet , Jesper Lykke Jacobsen , Rafael I. Nepomechie

We present a unified treatment of exact solutions for a class of four quantum mechanical models, namely the singular anharmonic potential, the generalized quantum isotonic oscillator, the soft-core Coulomb potential, and the…

Mathematical Physics · Physics 2015-06-03 Davids Agboola , Yao-Zhong Zhang

The one dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric viewpoint by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and…

Strongly Correlated Electrons · Physics 2008-12-18 You-Quan Li , Micheal Ma , Da-Ning Shi , Fu-Chun Zhang

We present a numerical method based on real-space renormalization that outputs the exact ground space of "frustration-free" Hamiltonians. The complexity of our method is polynomial in the degeneracy of the ground spaces of the Hamiltonians…

Strongly Correlated Electrons · Physics 2013-09-23 Adrian E. Feiguin , Rolando D. Somma , Cristian D. Batista

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