Correlation functions of the XXZ Heisenberg spin chain: Bethe ansatz approach

2009 ◽  
pp. 383-408
Author(s):  
Jean Michel Maillet
Keyword(s):  
Bethe Ansatz ◽  
Correlation Functions ◽  
Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Ansatz Approach

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 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.

scholarly journals Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Charles B. Thorn
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Spin Chain ◽  
Discrete Dynamical System ◽  
Heisenberg Spin ◽  
Free Fermions ◽  
Heisenberg Spin Chain ◽  
Delta Sigma ◽  
Special Cases ◽  
Quantized String

Abstract Although the energy spectrum of the Heisenberg spin chain on a circle defined by$$ H=\frac{1}{4}\sum \limits_{k=1}^M\left({\sigma}_k^x{\sigma}_{k+1}^x+{\sigma}_k^y{\sigma}_{k+1}^y+\Delta {\sigma}_k^z{\sigma}_{k+1}^z\right) $$ H = 1 4 ∑ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether M ∈ 4ℕ + r, where r = −1, 0, 1, 2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M1< M and M − M1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case ∆ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R0. We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for ∆ ≠ 0 is a change in the compactification radius R0→ R∆. As ∆ → −1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.

Sign in / Sign up

Export Citation Format

Share Document