Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons

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.