Scalar Products in Twisted XXX Spin Chain. Determinant Representation

@article{Belliard2019ScalarPI,
  title={Scalar Products in Twisted XXX Spin Chain. Determinant Representation},
  author={Samuel Belliard and Nikita Andreevich Slavnov},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2019}
}
  • S. Belliard, N. Slavnov
  • Published 17 June 2019
  • Mathematics
  • Symmetry, Integrability and Geometry: Methods and Applications
We consider XXX spin-$1/2$ Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case, we obtain a determinant representation for the norm of on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix. 

Why scalar products in the algebraic Bethe ansatz have determinant representation

Abstract We show that the scalar products of on-shell and off-shell Bethe vectors in the algebralic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this

Scalar product for the XXZ spin chain with general integrable boundaries * * Dedicated to the memory of Omar Foda.

We calculate the scalar product of Bethe states of the XXZ spin- 12 chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe

Overlap between usual and modified Bethe vectors

We consider the overlap of Bethe vectors of the XXX spin chain with a diagonal twist and the modified Bethe vectors with a general twist. We find a determinant representation for this overlap under

Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary

We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero–Moser systems associated with root systems of classical Lie algebras B N , C N , D N to the

Correlation functions by separation of variables: the XXX spin chain

We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg

Quantum-classical correspondence for supersymmetric Gaudin magnets with boundary

We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the

Wave functions and scalar products in the Bethe ansatz

Les modeles integrables sont des modeles physiques pour lesquels certaines quantites peuvent etre calculees de maniere exacte, sans recours aux methodes de perturbations. Ces modeles tres

Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields

In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ

References

SHOWING 1-10 OF 42 REFERENCES

Scalar product of twisted XXX modified Bethe vectors

We consider closed XXX spin chains with broken total spin symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on

Modified Algebraic Bethe Ansatz: Twisted XXX Case

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at

Form factors of the XXZ Heisenberg spin-1/2 finite chain

The open XXX spin chain in the SoV framework: scalar product of separate states

We consider the XXX open spin-1/2 chain with the most general non-diagonal boundary terms, that we solve by means of the quantum separation of variables (SoV) approach. We compute the scalar products

An inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin

An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of

Integral representations for correlation functions of the XXZ chain at finite temperature

We derive a novel multiple integral representation for a generating function of the σz–σz correlation functions of the spin- XXZ chain at finite temperature and finite, longitudinal magnetic field.

Off-diagonal Bethe ansatz and exact solution of a topological spin ring.

TLDR
A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry and it is found that the excitation spectrum shows a nontrivial topological nature.