Fermionic quantum dimer and fully-packed loop models on the square lattice

TL;DR

This paper studies fermionic quantum dimer and fully-packed loop models on a square lattice, revealing fluctuationless states, addressing the sign problem, and connecting the models to U(1) gauge theory and quantum electrodynamics.

Contribution

It introduces a detailed analysis of fermionic models on the square lattice, including sign problem mitigation and connections to gauge theories.

Findings

Identification of fluctuationless states due to fermionic statistics

Sign problem can be gauged away for certain states

Mapping to U(1) lattice gauge theory and quantum electrodynamics

Abstract

We consider fermionic fully-packed loop and quantum dimer models which serve as effective low-energy models for strongly correlated fermions on a checkerboard lattice at half and quarter filling, respectively. We identify a large number of fluctuationless states specific to each case, due to the fermionic statistics. We discuss the symmetries and conserved quantities of the system and show that for a class of fluctuating states in the half-filling case, the fermionic sign problem can be gauged away. This claim is supported by numerical evaluation of the low-lying states and can be understood by means of an algebraic construction. The elimination of the sign problem then allows us to analyze excitations at the Rokhsar-Kivelson point of the models using the relation to the height model and its excitations, within the single-mode approximation. We then discuss a mapping to a U(1) lattice gauge theory which relates the considered low-energy model to the compact quantum electrodynamics in 2+1 dimensions. Furthermore, we point out consequences and open questions in the light of these results.