We present the influences of electronic and magnetic correlations and doping evolution on the groundstate properties of recently discovered superconductor Ba$_{2}$CuO$_{4-delta}$ by utilizing the Kotliar-Ruckenstein slave boson method. Starting with
an effective two-orbital Hubbard model (Scalapino {it et al.} Phys. Rev. {bf B 99}, 224515 (2019)), we demonstrate that with increasing doping concentration, the paramagnetic (PM) system evolves from two-band character to single-band ones around the electron filling n=2.5, with the band nature of the $d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$ orbitals to the $d_{x^{2}-y^{2}}$ orbital, slightly affected when the electronic correlation U varies from 2 to 4 eV. Considering the magnetic correlations, the system displays one antiferromagnetically metallic (AFM) phase in $2<n<2.16$ and a PM phase in $n>2.16$ at U=2 eV, or two AFM phases in $2<n<2.57$ and $2.76<n<3$, and a PM phase in $2.57<n<2.76$ respectively, at U=4 eV. Our results show that near realistic superconducting state around n=2.6 the intermediate correlated Ba$_{2}$CuO$_{3,2}$ should be single band character, and the s-wave superconducting pairing strength becomes significant when U$>$2 eV, and crosses over to d-wave when U$>$2.2 eV.
Searching for spin liquids on the honeycomb J1-J2 Heisenberg model has been attracting great attention in the past decade. In this Paper we investigate the topological properties of the J1-J2 Heisenberg model by introducing nearest-neighbour and next
-nearest-neighbour bond parameters. We find that there exist two topologically different phases in the spin disordered regime 0.2<J2/J1<0.5: for J2/J1<0.32, the system is a zero-flux spin liquid which is topological trivial and gapless; for J2/J1>0.32, it is a pi-flux chiral spin liquid, which is topological nontrivial and gapped. These results suggest that there exist two topologically different spin disorder phases in honeycomb J1-J2 Heisenberg model.
We study a set of exactly soluble spin models in one and two dimensions for any spin $S$. Its ground state, the excitation spectrum, quantum phase transition points, as well as dimensional crossover are determined.
We study a set of exactly soluble net spin models. There exist two kinds of ground state, one is a complete dimerized state, and the other one is the ground state of corresponding spin-1 model. For the excitation gap, various phases were discovered and determined.
