scholarly journals Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots

2021 ◽  
Author(s):  
Nikolai Kitanine ◽  
◽  
Giridhar Kulkarni ◽  
◽  
◽  
...  
Keyword(s):  
Bethe Ansatz ◽  
Thermodynamic Limit ◽  
Spin Chain ◽  
Form Factors ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Bethe Equations ◽  
Treat All ◽  
Ansatz Approach

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.

scholarly journals Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 352
Author(s):  
Nenad Manojlović ◽  
Igor Salom
Keyword(s):  
Bethe Ansatz ◽  
Generating Function ◽  
Periodic Case ◽  
Gaudin Model ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Boundary Terms ◽  
Reflection Matrix ◽  
Bethe Equations

In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.

scholarly journals The equilibrium landscape of the Heisenberg spin chain

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Enej Ilievski ◽  
Eoin Quinn
Keyword(s):  
Spin Chain ◽  
Local Equilibrium ◽  
Functional Integral ◽  
Equilibrium States ◽  
Quantum Model ◽  
Full Generality ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Ansatz Approach ◽  
Integrable Quantum Model

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 frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical \mathcal{Y}𝒴-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

Bethe ansatz for an open Heisenberg spin chain with impurity

1994 ◽  
Vol 33 (3) ◽  
pp. 679-685
Author(s):  
Nibedita Bhattacharya ◽  
A. Roy Chowdhury
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

scholarly journals Factorization of Multiparticle Scattering in the Heisenberg Spin Chain

1997 ◽  
Vol 12 (34) ◽  
pp. 2591-2598 ◽  
Author(s):  
Anastasia Doikou ◽  
Luca Mezincescu ◽  
Rafael I. Nepomechie
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Antiferromagnetic Spin ◽  
Multiparticle Scattering ◽  
Explicit Proof

We give an explicit proof within the framework of the Bethe ansatz/string hypothesis of the factorization of multiparticle scattering in the antiferromagnetic spin-1/2 Heisenberg spin chain, for the case of three particles.

INTEGRABLE XYZ HAMILTONIAN WITH NEXT-NEAREST-NEIGHBOR INTERACTION

1999 ◽  
Vol 13 (07) ◽  
pp. 847-858
Author(s):  
YUN-ZHONG LAI ◽  
ZHAN-NING HU ◽  
J. Q. LIANG ◽  
FU-CHO PU
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Nearest Neighbor ◽  
Open Boundary ◽  
Limit Case ◽  
Neighbor Interaction ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Impurity Model ◽  
The Cross

In this paper, we construct a Hamiltonian of the impurity model with next-nearest-neighbor interaction within the framework of the open boundary Heisenberg XYZ spin chain. This impurity model is an exactly solved one and it degenerates to the integrable XXZ impurity model under the triangular limit. It is the first approach to add the impurities and next-nearest-neighbor interaction to the integrable completely anisotropic Heisenberg spin chain. We find also that the impurity parameters in the bulk are real when the cross parameter is imaginary for the Hermitian Hamiltonian, or vice versa, when the next-nearest-neighbor interaction is introduced. The eigenvalue of the Hamiltonian and the Bethe ansatz equations for the trigonometric limit case are derived also.

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