TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.4.090
TI  - The open XYZ spin 1/2 chain: Separation of variables and scalar products for boundary fields related by a constraint
PY  - 2025/10/08
UR  - https://www.scipost.org/SciPostPhys.19.4.090
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 4
SP  - 090
A1  - Niccoli, Giuliano
AU  - Terras, Véronique
AB  - We consider the open XYZ spin chain with boundary fields. We solve the model by the new Separation of Variables approach introduced in [J. M. Maillet and G. Niccoli, J. Stat. Mech.: Theory Exp. 094020 (2019)]. In this framework, the transfer matrix eigenstates are obtained as a particular sub-class of the class of so-called separate states. We consider the problem of computing scalar products of such separate states. As usual, they can be represented as determinants with rows labelled by the inhomogeneity parameters of the model. We notably focus on the special case in which the boundary parameters parametrising the two boundary fields satisfy one constraint, hence enabling for the description of part of the transfer matrix spectrum and eigenstates in terms of some elliptic polynomial $Q$-solution of a usual $TQ$-equation. In this case, we show how to transform the aforementioned determinant for the scalar product into some more convenient form for the consideration of the homogeneous and thermodynamic limits: as in the open XXX or XXZ cases, our result can be expressed as some generalisation of the so-called Slavnov determinant.
ER  -

@Article{10.21468/SciPostPhys.19.4.090,
	title={{The open XYZ spin 1/2 chain: Separation of variables and scalar products for boundary fields related by a constraint}},
	author={Giuliano Niccoli and Veronique Terras},
	journal={SciPost Phys.},
	volume={19},
	pages={090},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.4.090},
	url={https://scipost.org/10.21468/SciPostPhys.19.4.090},
}