We consider a Hubbard-like model of strongly interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half filling. The problem of a single stripe can be mapped to fermions in one dimension, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of a few stripes, finding that they repel and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into a particle-rich phase and a hole-rich liquid, we evaluate the liquid's equation of state, finding that the stripe-array is not stable for bosons but is possibly stable for fermions.
The interplay of spin and motional degrees of freedom forms a key element in explaining stripe formation accompanied by sublattice reversal of local antiferromagnetic ordering in interacting fermionic models. A long-standing question aims to relate pairing to stripe formation, intending to discern the applicability of simple models that observe this phenomenon in understanding cuprate physics. By departing from fermionic statistics, we show that the formation of stripes is rather generic, allowing one to unveil its competition with superfluid behavior. To that end, we use a combination of numerical methods to solve a model of interacting hardcore bosons in ladder geometries, finding that once stripes are formed, either via external pinning or spontaneously, a sublattice reversal (
π-phase shift) of \textit{charge} ordering occurs, suppressing the superfluid weight. Lastly, we show that when the Cooper pairs are not local, as in the attractive Hubbard model with finite interactions, auxiliary-field quantum Monte Carlo calculations show evidence of fluctuating stripes, but these are seen to coexist with superfluidity. Our results corroborate the picture that static stripes cannot be reconciled with pairing, unlike the case of fluctuating ones.