The differences between the XXZ model with topological and periodical boundary conditions were compared by studying their entanglement, quantum discord, and critical temperature above which the entanglement vanishes. It shows that the different boundary conditions mainly affect bipartite quantum correlations of the boundary spins rather than that of other spin pairs. The topological boundary spins can protect entanglement and discord against strong magnetic fields while the periodical boundary spins can protect them against nonuniform magnetic fields. Compared with the periodical XXZ model, the critical temperature is significantly improved for the topological XXZ model. The topological XXZ model also allows us to improve significantly its critical temperature by increasing the strength of magnetic field, which is not feasible for the periodical XXZ model. It is therefore more promising for preparing entangled states at high temperature in the topological XXZ model.The differences between the XXZ model with topological and periodical boundary conditions were compared by studying their entanglement, quantum discord, and critical temperature above which the entanglement vanishes. It shows that the different boundary conditions mainly affect bipartite quantum correlations of the boundary spins rather than that of other spin pairs. The topological boundary spins can protect entanglement and discord against strong magnetic fields while the periodical boundary spins can protect them against nonuniform magnetic fields. Compared with the periodical XXZ model, the critical temperature is significantly improved for the topological XXZ model. The topological XXZ model also allows us to improve significantly its critical temperature by increasing the strength of magnetic field, which is not feasible for the periodical XXZ model. It is therefore more promising for preparing entangled states at high temperature in the topological XXZ model.

Scientific ReportsJan 31, 20197 citations

Spin 1/2 in a Uniform Magnetic Field

Brian P. Anderson

SPIE eBooksSep 12, 20190 citations

Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field

Ke-Tao Guo, M. M. Liang, Hong-Yu Xu +1 more

Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.

Journal of Physics A Mathematical and TheoreticalNov 22, 201015 citations

Magnetic-field control of interactions in alkaline-earth Rydberg atoms and applications to {\it XXZ} models

Masaya Kunimi, Takafumi Tomita

We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, ${}^{88}$ Sr and ${}^{174}$ Yb. Considering the pair of Rydberg states $|ns,{}^3S_1,m_J\rangle$ and $|(n+1)s,{}^3S_1,m_J\rangle$ , we show that the effective Hamiltonian takes the form of an {\it XXZ}-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A {\bf 112}, L051301 (2025)]. We find that the behavior of the anisotropy parameter for ${}^{174}$ Yb at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in ${}^{174}$ Yb. We systematically calculate the interaction parameters of the {\it XXZ} model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded {\it XXZ} model can be realized in ${}^{174}$ Yb systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, ${}^{88}$Sr and ${}^{174}$Yb. Considering the pair of Rydberg states $|ns,{}^3S_1,m_J\rangle$ and $|(n+1)s,{}^3S_1,m_J\rangle$, we show that the effective Hamiltonian takes the form of an {\it XXZ}-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A {\bf 112}, L051301 (2025)]. We find that the behavior of the anisotropy parameter for ${}^{174}$Yb at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in ${}^{174}$Yb. We systematically calculate the interaction parameters of the {\it XXZ} model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded {\it XXZ} model can be realized in ${}^{174}$Yb systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.

cond-mat.quant-gasCross-listedarXiv:2604.21206Apr 24, 20260 citations

Solvable case of a spin-1 model in a magnetic field

R. Shankar

Physics Letters ASep 1, 198620 citations

We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms,

{}^{88}

Sr and

{}^{174}

Yb. Considering the pair of Rydberg states

|ns,{}^3S_1,m_J\rangle

and

|(n+1)s,{}^3S_1,m_J\rangle

, we show that the effective Hamiltonian takes the form of an {\it XXZ}-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A {\bf 112}, L051301 (2025)]. We find that the behavior of the anisotropy parameter for

{}^{174}

Yb at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in

{}^{174}

Yb. We systematically calculate the interaction parameters of the {\it XXZ} model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded {\it XXZ} model can be realized in

{}^{174}

Yb systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.