# 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} }

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.

## 10 Citations

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## References

SHOWING 1-10 OF 42 REFERENCES

### Scalar product of twisted XXX modified Bethe vectors

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2018

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…

### Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

- Mathematics
- 2013

### Modified Algebraic Bethe Ansatz: Twisted XXX Case

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2018

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…

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

- Mathematics
- 2017

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

- Mathematics, Physics
- 2013

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

- Physics
- 2004

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.

- PhysicsPhysical review letters
- 2013

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.