Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm

Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit, N → ∞, in terms of the N spin- 1 / 2 physical spins of the spin- 1 / 2 X X Z chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies Δ > 1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin- 1 / 2 X X Z chain’s continuous S U q ( 2 ) symmetry parameterized by q = Δ + Δ 2 − 1 ∈ ] 1 , ∞ ] and associated with q-spin S q. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length n that have no spinon representation, contribute to the dynamical properties of the spin- 1 / 2 X X Z chain with anisotropy Δ > 1 and for n = 1 , 2 , 3 were experimentally identified and realized in the zigzag materials SrCo 2V 2O 8 and BaCo 2V 2O 8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous S U q ( 2 ) symmetry reveals that for anisotropy Δ > 1 the Bethe strings of length n = 1 , 2 , 3 , … describe a number n of physical-spins S q = 0 singlet pairs that for n > 1 are bound within a S q = 0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin- 1 / 2 X X Z chain in a longitudinal magnetic field and the spin chains in SrCo 2V 2O 8 is one of the issues addressed in this paper. In addition, the S U q ( 2 ) symmetry imposes that only 2 S q out of the N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento [“Diffusive spin