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

@article{Kitanine2021FormFO,
  title={Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots},
  author={N. Kitanine and Giridhar Kulkarni},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2021}
}
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… 

References

SHOWING 1-10 OF 44 REFERENCES
Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant
On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that
Form factors of the XXZ Heisenberg spin-1/2 finite chain
Asymptotic analysis of the form-factors of quantum spin chains
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact
Form factors of bound states in the XXZ chain
This work focuses on the calculation of the large-volume behaviour of form factors of local operators in the XXZ spin-1/2 chain taken between the ground state and an excited state containing bound
The thermodynamic limit of particle–hole form factors in the massless XXZ Heisenberg chain
We study the thermodynamic limit of the particle–hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly
A thermal form factor series for the longitudinal two-point function of the Heisenberg–Ising chain in the antiferromagnetic massive regime
We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the
Analysis of the Bethe ansatz equations of the XXZ model
...
...