The ferrimagnetism and quantum phase transition of a bipartite lozenge periodic Anderson-like organic polymer, in which the localized f electrons hybridize with the odd site conduction orbitals, are investigated by means of Green＇s function theory. The ground state turns out to be gapless ferrimagnetism. At a finite temperature, the ferrimagnetic-to- paramagnetic phase transition takes place. The Kondo screenings and Ruderman-Kittel-Kasuya-Yosida （RKKY） inter- action can reduce and increase the transition temperature, respectively. Two Kondo screenings compete with each other, giving rise to the localized f electron spin screened antiferromagnetically. Accordingly, in a magnetic field, all spins are aligned along the chain easily, which is associated with metal-insulator transition. Furthermore, in a temperature-field plane, we reveal the gapless and spin polarized phases, which are characterized by susceptibility and specific heat, and whose behaviours are determined by the competition between the up-spin and down-spin hole excitations.
The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green＇s function theory.（i） For the completely antiferromagnetic（AFM） alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic（FM） phases,as a result of the intra-cluster spin-singlet competition. Furthermore, the Gr ¨uneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases.（ii） For the antiferromagnetically coupled FM alternating chains,the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally.Nevertheless, the M–h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.
