Quasi-local Frustration-Free Free Fermions

TL;DR

This paper explores how relaxing the finite-range condition in frustration-free free fermion models to include exponential and power-law decays enables the realization of topological insulators, gapless metals, and clarifies properties of such systems.

Contribution

It demonstrates that exponentially decaying hoppings can produce gapped topological phases and power-law decays can lead to gapless metals in frustration-free free fermion models.

Findings

Exponential decay hoppings realize Chern insulators.

Power-law decay hoppings produce gapless metals with inverse size scaling.

Relaxing finite-range conditions broadens the class of frustration-free systems.

Abstract

Recent studies have revealed that frustration-free models, expressed as sums of finite-range interactions or hoppings, exhibit several properties markedly different from those of frustrated models. In this work, we demonstrate that, by relaxing the finite-range condition to allow for exponentially decaying hoppings, one can build gapped frustration-free systems that realize Chern insulators as well as quasi-degenerate ground states with finite-size splittings. Moreover, by permitting power-law decaying hoppings, we also construct a gapless band metal whose finite-size gap scales inversely with the system size $L$. These findings serve as an important step toward clarifying the general properties of frustration-free systems and those represented by tensor network states.