To investigate relations between long-range antiferromagnetic (AF) order, superconductivity and two-particle triplet collective excitations we consider a modified two dimensional $t\ensuremath{-}J$ model at doping close to half filling. The model includes additional hopping ${J}^{\ensuremath{''}}$ and nearest sites Coulomb repulsion V. The additional parameters allow us to control closeness of the system to the AF instability. We demonstrate the possibility of coexistence of long-range AF order and $d\ensuremath{-}g$-wave superconductivity. In the phase with long-range AF order we find, analytically, superconducting gaps and spin-wave renormalization. We demonstrate that at approaching the point of the AF instability the spin-triplet collective excitation arises with energy below the superconducting gap.
We investigate the ionic Hubbard model (IHM) at half-filling in the limit of strong correlations and large ionic potential. The low-energy effective Hamiltonian in this limit, obtained by a similarity transformation, is a modified $t\ensuremath{-}J$ model with effective second-neighbor hopping terms. We explore the possibilities of
d-wave pairing and extended
s-wave pairing superconducting (SC) phases on a two-dimensional square lattice at zero temperature within a Gutzwiller projected renormalized mean-field theory. In the sector of solutions that forbid spin-ordering, the system shows a finite nonzero
d-wave as well as extended
s-wave pairing amplitude for $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}U\ensuremath{\gg}t$. The width of the superconducting phase in $U\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ regime shrinks with increase in
U and $\mathrm{\ensuremath{\Delta}}$, though the extended
s-wave pairing phase is higher in energy than the
d-wave pairing superconducting phase. But in a spin-resolved renormalized mean-field calculation, which allows for an antiferromagnetic (AF) order along with the
d-wave or extended
s-wave pairing, the SC phase is no longer viable and the system shows a direct transition from an AF ordered phase to a paramagnetic band insulator. Except for a thin sliver of a half-metallic AF phase close to the AF transition point, most of the AF ordered phase is a Mott insulator. We benchmarked the AF Mott insulator to band insulator transition within the Gutzwiller projected renormalized mean-field theory against the dynamical mean-field theory solved using continuous time quantum Monte Carlo. Our work suggests that the ground-state phase diagram of the IHM at half-filling in the limit of extreme correlations does not have any SC phase. The SC phase seen in the paramagnetic sector is a metastable phase, being higher in energy than the AF Mott insulator phase.
Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.