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

TL;DR

This paper investigates a 2D lattice model of spinless fermions and hardcore bosons, revealing stripe formations as a doping mechanism, analyzing their excitations, interactions, and stability, with implications for phase separation.

Contribution

It introduces a detailed analysis of stripe structures and their interactions in a 2D strongly-interacting fermion/boson system, including stability conditions.

Findings

Stripes form as a favorable doping pattern below half-filling.

Single stripe excitations can be understood via a spin-1/2 chain model.

Stripe interactions decay as hardcore particles in one dimension.

Abstract

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 a spin-1/2 chain, 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 two, three, and four 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 particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.