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arXiv · 1101.0335

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

Frank Pollmann·Joseph J. Betouras·Kirill Shtengel·Peter Fulde
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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.

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Frank Pollmann, Joseph J. Betouras, Kirill Shtengel, Peter Fulde. 2011-01-01. Fermionic quantum dimer and fully-packed loop models on the square lattice. https://doi.org/10.1103/physrevb.83.155117

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