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We examine the effective field theory of the Bethe ansatz integrable Heisenberg antiferromagnetic spin chains. It shows that the quantum critical theories for the integer spin-S chains should be characterized by the SO(3)level-S…

Strongly Correlated Electrons · Physics 2012-11-26 Zheng-Xin Liu , Guang-Ming Zhang

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

This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the $OSp(3|2)$ superalgebra. The finite-size properties of the eigenspectra are computed by solving…

Statistical Mechanics · Physics 2019-07-25 Holger Frahm , Konstantin Hobuß , Márcio J. Martins

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 consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of…

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

We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell,…

Nuclear Theory · Physics 2008-11-26 A. B. Balantekin , J. H. de Jesus , Y. Pehlivan

We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has…

Other Condensed Matter · Physics 2009-11-13 Vyacheslav V. Stepanov , Gerhard Muller , Joachim Stolze

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…

Mathematical Physics · Physics 2013-08-23 Daniel Ueltschi

Using the well-known free-field formalism for quantum groups, we demonstrate in case of $A(n)_q$, that quantum group is naturally also a cluster variety. Widely used formulae for mutations are direct consequence of independence of group…

Quantum Algebra · Mathematics 2014-03-10 Alexandr Popolitov

We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…

Other Condensed Matter · Physics 2008-11-26 L. Amico , H. Frahm , A. Osterloh , G. A. P. Ribeiro

It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…

Quantum Physics · Physics 2021-02-09 Amin Naseri , Yutao Hu , Wenchen Luo

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we propose the Bethe ansatz solution for the transfer matrix eigenvalues for cases where…

High Energy Physics - Theory · Physics 2009-11-19 Rajan Murgan

In this paper, we show the integrability of spin-1/2 XXZ Heisenberg chain with two arbitrary spin boundary Impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these…

Condensed Matter · Physics 2009-10-31 Boyu Hou , Kangjie Shi , Ruihong Yue , Shaoyou Zhao

Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…

High Energy Physics - Theory · Physics 2008-11-26 Robert Oeckl

We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…

High Energy Physics - Theory · Physics 2021-01-20 Rafael I. Nepomechie , Ana L. Retore

The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer…

Mathematical Physics · Physics 2019-06-05 Guang-Liang Li , Junpeng Cao , Panpan Xue , Zhi-Rong Xin , Kun Hao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We introduce a family of quantum spin Hamiltonians on $\mathbb{Z}^2$ that can be regarded as perturbations of Kitaev's abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the…

Mathematical Physics · Physics 2023-11-16 Sven Bachmann , Bruno Nachtergaele , Siddharth Vadnerkar

We construct two quantum spin chains Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami…

Mathematical Physics · Physics 2010-02-03 Daniel Arnaudon

We present a pairing Hamiltonian of the Bardeen-Cooper-Schrieffer form which exhibits two quantum critical lines of deconfined excitations. This conclusion is drawn using the exact Bethe ansatz equations of the model which admit a class of…

Superconductivity · Physics 2017-10-19 Jon Links , Amir Moghaddam , Yao-Zhong Zhang

We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…

High Energy Physics - Theory · Physics 2025-08-25 Barak Gabai , Victor Gorbenko , Jiaxin Qiao , Bernardo Zan , Aleksandr Zhabin