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Related papers: Bethe ansatz solution of an integrable, non-Abelia…

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Orthosympletic Hamiltonians derived from representations of the Temperley-Lieb algebra are presented and solved via the coordinate Bethe Ansatz. The spectra of these Hamiltonians are obtained using open and closed boundary conditions.

High Energy Physics - Theory · Physics 2009-10-31 A. Lima-Santos

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Mathematical Physics · Physics 2015-06-09 Yupeng Wang , Wen-Li Yang , Junpeng Cao , Kangjie Shi

Anyons obeying fractional exchange statistics arise naturally in two dimensions: hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent…

Quantum Gases · Physics 2024-03-27 Sebastian Nagies , Botao Wang , A. C. Knapp , André Eckardt , N. L. Harshman

We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…

Mathematical Physics · Physics 2017-02-20 Jens Bolte , George Garforth

We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations…

Strongly Correlated Electrons · Physics 2007-05-23 Luigi Amico , Andreas Osterloh , Ulrich Eckern

We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…

Other Condensed Matter · Physics 2010-04-05 V. Caudrelier , N. Crampe

We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the $gl(2)$-invariant $R$-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins…

Mathematical Physics · Physics 2019-09-18 G. Santos

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

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is an example of the so-called quasi-exactly solvable models. The solvable parts of its spectrum was previously solved from the…

High Energy Physics - Theory · Physics 2009-11-07 Chun-Ming Chiang , Choon-Lin Ho

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…

Statistical Mechanics · Physics 2011-03-07 Holger Frahm , Jan H. Grelik , Alexander Seel , Tobias Wirth

We study the quantum integrable spin chain model associated with the twisted $D_2^{(2)}$ algebra (or simply the $D_2^{(2)}$ model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two…

Mathematical Physics · Physics 2025-05-19 Pengcheng Lu , Junpeng Cao , Wen-Li Yang , Ian Marquette , Yao-Zhong Zhang

We study in detail the analytic properties of the Thermodynamic Bethe Ansatz (TBA) equations for the anomalous dimensions of composite operators in the planar limit of the 3D N=6 superconformal Chern-Simons gauge theory and derive…

High Energy Physics - Theory · Physics 2015-06-16 Andrea Cavaglia' , Davide Fioravanti , Roberto Tateo

In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain…

Statistical Mechanics · Physics 2022-07-29 Marius de Leeuw , Chiara Paletta

I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific…

High Energy Physics - Theory · Physics 2007-05-23 L. D. Faddeev

We introduce a new type of models for two-component systems in one dimension subject to exact solutions by Bethe ansatz, where the interspecies interactions are tunable via Feshbach resonant interactions. The applicability of Bethe ansatz…

Quantum Gases · Physics 2019-02-20 Tianhao Ren , Igor Aleiner

In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a $\delta$-function barrier. Only half of the Hilbert…

Mathematical Physics · Physics 2025-11-19 Maxim Olshanii , Mathias Albert , Gianni Aupetit-Diallo , Patrizia Vignolo , Steven G. Jackson

A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied…

High Energy Physics - Theory · Physics 2009-10-30 Julio Abad , Miguel Rios

We study the Hilbert space of the Class 5 model described in arXiv:1904.12005. Despite being integrable, neither its transfer matrix nor its Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz does not provide the…

High Energy Physics - Theory · Physics 2023-12-11 Juan Miguel Nieto García

The double row transfer matrix of the open O(N) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is…

Mathematical Physics · Physics 2018-09-19 Tamas Gombor

By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe ansatz to diagonalize the Liouvillian ${\mathcal…

Statistical Mechanics · Physics 2025-02-11 Vincenzo Alba