English
Related papers

Related papers: Algebraic Bethe Circuits

200 papers

We propose applying the adiabatic algorithm to prepare high-energy eigenstates of integrable models on a quantum computer. We first review the standard adiabatic algorithm to prepare ground states in each magnetization sector of the…

Quantum Physics · Physics 2026-03-18 Maximilian Lutz , Lorenzo Piroli , Georgios Styliaris , J. Ignacio Cirac

We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 G. A. P. Ribeiro , M. J. Martins

We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we…

Mathematical Physics · Physics 2017-11-28 Rouven Frassek

We present the exact solution of a family of fragmented Bose-Hubbard models and represent the models as graphs with the condensates in the vertices. The models are solved by the algebraic Bethe ansatz method. We show that the models have…

Exactly Solvable and Integrable Systems · Physics 2021-05-31 Gilberto N. Santos Filho

We derive exactly scalar products and form factors for integrable higher-spin XXZ chains through the algebraic Bethe-ansatz method. Here spin values are arbitrary and different spins can be mixed. We show the affine quantum-group symmetry,…

Statistical Mechanics · Physics 2011-07-06 Tetsuo Deguchi , Chihiro Matsui

The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and…

Mathematical Physics · Physics 2017-04-12 Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-1/2 XXZ quantum spin chain with either open or closed boundary conditions. The algorithm…

Quantum Physics · Physics 2024-10-30 David Raveh , Rafael I. Nepomechie

The quantum 2-component DS1 system was reduced to two 1D many-body problems with $\delta-$function interactions, which were solved by Bethe ansatz. Using the ansatz in ref.[1] and introducing symmetric and antisymmetric Young operators of…

Condensed Matter · Physics 2007-05-23 Yi Cheng , Mu-Lin Yan , Bao-Heng Zhao

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based…

High Energy Physics - Theory · Physics 2016-07-26 Fedor Levkovich-Maslyuk

We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…

High Energy Physics - Theory · Physics 2011-07-19 C. Destri , H. J. de Vega

A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…

Mathematical Physics · Physics 2024-12-18 Guang-Liang Li , Junpeng Cao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

To each representation of the elliptic quantum group $E_{\tau,\eta}(sl_2)$ is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz method. Special cases of this…

q-alg · Mathematics 2009-10-30 Giovanni Felder , Alexander Varchenko

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

High Energy Physics - Theory · Physics 2007-05-23 A. V. Zabrodin

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

The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to…

High Energy Physics - Theory · Physics 2025-12-02 Yunfeng Jiang , Yi-Chao Liu , Yuan Miao , Zi-Xi Tan

Quantum computers can be used for the solution of various problems of mathematical physics. In the present paper, we consider a discretized version of the heat equation and address its solution on quantum computer using variational Anzats…

Quantum Physics · Physics 2024-04-23 N. M. Guseynov , W. V. Pogosov , A. V. Lebedev

Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…

High Energy Physics - Theory · Physics 2016-09-06 Anjan Kundu

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

The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions…

High Energy Physics - Theory · Physics 2013-07-10 Rafael I. Nepomechie , Chunguang Wang

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