Correlated Fermions on a Checkerboard Lattice

TL;DR

This paper studies a model of strongly correlated spinless fermions on a checkerboard lattice, revealing fluctuationless states, addressing the fermionic sign problem, and analyzing excitations at the Rokhsar-Kivelson point.

Contribution

It maps the fermionic model to a quantum loop model, identifies fluctuationless states, and demonstrates that the sign problem can be gauged away for certain states.

Findings

Identification of fluctuationless states unique to fermions

Fermionic sign problem can be gauged away in some states

Detailed analysis of excitations at the Rokhsar-Kivelson point

Abstract

A model of strongly correlated spinless fermions hopping on a checkerboard lattice is mapped onto a quantum fully-packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states, the fermionic sign problem can be gauged away. This claim is supported by numerically evaluating the energies of the low-lying states. Furthermore, we analyze in detail the excitations at the Rokhsar-Kivelson point of this model thereby using the relation to the height model and the single-mode approximation.