English
Related papers

Related papers: The Algebraic Bethe Ansatz and Tensor Networks

200 papers

We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s=1/2 Heisenberg model to calculate and numerically…

Strongly Correlated Electrons · Physics 2009-11-07 Daniel Biegel , Michael Karbach , Gerhard Muller

We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…

Mathematical Physics · Physics 2024-06-12 Allan John Gerrard

The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows…

Mathematical Physics · Physics 2007-05-23 V. I. Inozemtsev

A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis…

q-alg · Mathematics 2009-10-28 Takashi Takebe

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, a systematic method for retrieving the Bethe-type eigenstates of integrable models without obvious reference state is developed by employing certain…

Mathematical Physics · Physics 2015-07-16 Xin Zhang , Yuan-Yuan Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Bethe Ansatz solutions of the open spin-1/2 integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed. We use these solutions to compute the…

High Energy Physics - Theory · Physics 2008-11-26 Rajan Murgan , Rafael I. Nepomechie , Chi Shi

The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the…

High Energy Physics - Theory · Physics 2015-05-20 Matthias Staudacher

We present in this paper a comprehensive introduction to the algebraic Bethe Ansatz, taking as examples the six-vertex model with periodic and non-periodic boundary conditions. We propose a diagrammatic representation of the commutation…

Combinatorics · Mathematics 2018-04-03 R. S. Vieira , A. Lima-Santos

An analytic Bethe ansatz is carried out related to tensor-like representations of the type II Lie superalgebras B(r|s)=osp(2r+1|2s) (r > -1, s >0) and D(r|s)=osp(2r|2s) (r >1, s >0). We present eigenvalue formulae of transfer matrices in…

Mathematical Physics · Physics 2009-12-15 Zengo Tsuboi

A new exactly solvable one-dimensional spin-3/2 Heisenberg model with SO(5)-invariance is proposed. The eigenvalues and Bethe ansatz equations of the model are obtained by using the nested algebraic Bethe ansatz approach. Several exotic…

Strongly Correlated Electrons · Physics 2009-07-08 Yuzhu Jiang , Junpeng Cao , Yupeng Wang

The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$\frac{1}{2}$ chain is investigated. Numerical calculations shows that, for this state,…

Mathematical Physics · Physics 2018-06-20 S. Belliard , A. Faribault

We investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called "integrable initial/final states". These states satisfy a special integrability constraint, and they are closely related to…

Statistical Mechanics · Physics 2021-05-05 Tamás Gombor , Balázs Pozsgay

We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 G. A. P. Ribeiro , M. J. Martins , W. Galleas

We investigate entanglement properties of the excited states of the spin-1/2 Heisenberg (XXX) chain with isotropic antiferromagnetic interactions, by exploiting the Bethe ansatz solution of the model. We consider eigenstates obtained from…

Strongly Correlated Electrons · Physics 2014-10-28 Jan Mölter , Thomas Barthel , Ulrich Schollwöck , Vincenzo Alba

We study the XXZ Heisenberg model in a longitudinal magnetic field using a tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization…

Strongly Correlated Electrons · Physics 2020-03-10 Mykhailo V. Rakov , Michael Weyrauch

We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to the case of soliton non-preserving…

Mathematical Physics · Physics 2015-06-26 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , Eric Ragoucy

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.…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 V. Fridkin , Yu. Stroganov , D. Zagier

This paper is a continuation of [1], in which a set of matrix elements of local operators was computed for the XXZ spin-1/2 open chain with a particular case of unparallel boundary fields. Here, we extend these results to the more general…

Mathematical Physics · Physics 2025-08-01 G. Niccoli , V. Terras

An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in…

Mathematical Physics · Physics 2023-03-09 Pascal Baseilhac , Rodrigo A. Pimenta

We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit…

Condensed Matter · Physics 2008-11-26 Shao-shiung Lin , Shi-shyr Roan