2134/12753
Frank Pollmann
Kirill Shtengel
Joseph Betouras
Peter Fulde
Fermionic quantum dimer and fully-packed loop models on the square lattice
2013
Loughborough University
untagged
2013-07-15 11:24:37
article
https://repository.lboro.ac.uk/articles/journal_contribution/Fermionic_quantum_dimer_and_fully-packed_loop_models_on_the_square_lattice/9407789
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.