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

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journal contribution
posted on 2013-07-15, 11:24 authored by Frank Pollmann, Kirill Shtengel, Joseph BetourasJoseph Betouras, Peter Fulde
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.



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POLLMANN, F. ... et al, 2011. Fermionic quantum dimer and fully-packed loop models on the square lattice. Physical Review B - Condensed Matter and Materials Physics, 83 (155117), 11pp.


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