Competition between different long-distance superexchange couplings in a quadripartite spin-crossover molecular device

Long-distance superexchange coupling provides a powerful tool for scalable quantum processors required in quantum information and quantum computation. Quadripartite spin-crossover molecules are prototypical systems for studying novel quantum phenomena assisted by superexchange interactions. In this paper, we consider a quadripartite molecule where two central monomers are connected to two electrodes, whereas another two are side coupled to their neighboring central monomers. Numerical renormalization group results demonstrate that, when the energy level spacing between two central monomers $\mathrm{\ensuremath{\Delta}}$ turns on, spins on the two side monomers are organized ferromagnetically. The effective antiferromagnetic superexchange interaction between the side units and the electrodes then induces a long-distance ferromagnetic Ruderman-Kittel-Kasuya-Yosida interaction between two side monomers. For intermediate $\mathrm{\ensuremath{\Delta}}$, the linear conductance tends to reach its unitary limit in a moderate low-temperature regime due to a superexchange two-stage Kondo effect. When the hopping integral between two central monomers sweeps upwards, where $\mathrm{\ensuremath{\Delta}}$ is fixed at a small value, a quantum phase transition occurs. A long-distance antiferromagnetic exchange coupling between two side units is clarified, isolating the molecule from the electrodes with zero conductance. If $\mathrm{\ensuremath{\Delta}}$ is set to be an intermediate value, applying the hopping integral then triggers a singular quantum phase, where two central monomers are antiparallelly aligned, whereas two side ones are organized ferromagnetically, revealing well the competition between the above two kinds of long-distance superexchange couplings. Temperature-dependent images and numerical simulations confirm the above conclusions.