Correlated Fermions on a Checkerboard Lattice

A model of strongly correlated spinless fermions on a checkerboard lattice is mapped onto a quantum fully packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states the fermionic sign problem can be gauged away. This claim is supported by numerical evaluation of the low-lying states. Furthermore, we analyze excitations at the Rokhsar-Kivelson point of this model using the relation to the height model and the single-mode approximation.

Figure 1

(a) A configuration of fermions satisfying the “two per tetrahedron” rule and its representation in terms of FPLs. A smallest “flippable plaquette” is shaded (see text for details). (b–d) Fragments of possible “frozen” states: (b) is fluctuationless under any local ring exchanges while (c) and (d) are fluctuationless only for fermionic ring exchanges. (e) The long-range ordered squiggle state maximizing the number of three-dimer ring exchanges (shaded). (f) Analog of a plaquette phase, with three dimers predominantly fluctuating around shaded rectangles; shown dimers are not participating in these exchanges.

Figure 2

(a) Three different actions of the effective Hamiltonian on the topology of loop configurations. (b, c) Representation of configuration as fully packed directed loops.

Figure 3

GS energy and energies of lowest excited states of the effective Hamiltonian in sectors with different slopes (${\kappa }_x,0$). Left panel: Data from an exact diagonalization of $H_{\mathrm{eff}}$ on a 72 site cluster where the Fermi sign is taken into account. Right panel: Same data from a calculation with excluded Fermi signs.