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

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##### Citation

Pollmann, F., Betouras, J. J., Shtengel, K., & Fulde, P. (2011). Fermionic quantum
dimer and fully-packed loop models on the square lattice.* Physical Review B,* *83*(15):
155117.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-8D21-0

##### 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 and which are due to 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 a 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.