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Inspired by the recent experimental advances in cold atom quantum simulators, we explore the experimentally implemented bosonic t-t′-J model on the square lattice using large-scale density matrix renormalization group simulations. By tuning the doping level δ and hopping ratio t′/t, we uncover six distinct quantum phases, several of which go far beyond the conventional paradigm of phase-coherent superfluidity (SF) expected for bosonic systems. In particular, in the presence of antiferromagnetic (AFM) order, doped holes are tightly bound into pairs, giving rise to a pair density wave (PDW) phase at low doping and small |t′/t|, which is suppressed on the t′ < 0 side, resulting in a disordered PDW state that lacks coherence of either individual bosons or pairs. Upon further doping, bosons can regain phase coherence and form a SF* state, characterized by condensation at emergent incommensurate momenta concurrent with an incommensurate magnetic order. On the t′ > 0 side, the sign-induced kinetic frustration inherently disfavors local AFM correlations, leading to a phase separation in which doped holes cluster into ferromagnetic (FM) domains spatially separated by undoped AFM regions. Upon further doping, this inhomogeneous state evolves into a uniform SF + xy-FM phase. Finally, we propose a concrete experimental scheme to realize both signs of t′/t in Rydberg tweezer arrays, with an explicit mapping between model parameters and experimentally accessible regimes. Our results reveal competing and intertwined orders in doped antiferromagnets, which are relevant to central issues in high-Tc superconductivity, reflecting the frustrated interplay between doped holes and spin background. 

The Hubbard and closely relatedt-Jmodels are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extendedt-Jmodel on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the puret-Jmodel with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( $\delta =0.1\mathrm{to}0.2$), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping $t_2$suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates thet-Jmodel as a proper minimum model for the emergence of superconductivity in cuprate superconductors. 

We study local density of state (LDOS) oscillations arising from the scattering of electrons at atomic edge defects in topological insulator (TI) surfaces. To create edge scattering on the surface of a TI, we assume that half of its surface is covered with a semiconductor. In addition to modifying the TI states in the covered half, the presence of the semiconductor leads to a localized edge potential at the vacuum-semiconductor boundary. We study the induced LDOS by imposing time-reversal (TR) invariance and current conservation across the boundary. Additionally, we explore how the scattering of TI junctions with dissimilar spin textures and anisotropic Fermi velocities affect the modulations of the LDOS away from the junction edge. In all cases, for energies close to the Dirac point, we find that the decay envelope of the LDOS oscillations is insensitive to the scattering at the atomic edge defect, with a decay power given by 𝑥−3/2. Quantitative differences in the amplitude of these oscillations depend on the details of the interface and the spin textures, while the period of the oscillations is defined by the size of the Fermi surface.