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arXiv:cond-mat/0607202 · Physical Review Letters

Correlated Fermions on a Checkerboard Lattice

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

Published Oct 26, 2006• 34 citations
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Abstract

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.

DOI
10.1103/physrevlett.97.170407

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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.
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+12+12+1 dimensions. Furthermore, we point out consequences and open questions in the light of these results.
Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges ±e/2. We calculate quantum mechanical ground states, low–lying excitations and spectral functions of finite lattices by means of numerical diagonalization. The ground state of the most thorough-fully studied case, the criss-crossed checkerboard lattice, is degenerate and shows long–range order. Static fractional charges are confined by a weak linear force, most probably leading to bound states of large spatial extent. Consequently, the quasi-particle weight is reduced, which reflects the internal dynamics of the fractionally charged excitations. By using an additional parameter, we fine–tune the system to a special point at which fractional charges are manifestly deconfined—the so–called Rokhsar–Kivelson point. For a deeper understanding of the low–energy physics of these models and for numerical advantages, several conserved quantum numbers are identified.
We study the dynamical properties of spinless fermions on the checkerboard lattice. Our main interest is the limit of large nearest-neighbor repulsion VVV as compared with hopping $\ensuremath{\mid}t\ensuremath{\mid}$. The spectral functions show broad low-energy excitations which are due to the dynamics of fractionally charged excitations. Furthermore, it is shown that the fractional charges contribute to the electrical current density.
The quantum dimer and loop models attract great attention, partially because the fundamental importance in the phases and phase transitions emerging in these prototypical constrained systems, and partially due to their intimate relevance toward the on-going experiments on Rydberg atom arrays in which the blockade mechanism naturally enforces the local constraint. Here we show, by means of the sweeping cluster quantum Monte Carlo method, the complete ground state phase diagram of the fully packed quantum loop model on the square lattice. We find between the lattice nematic (LN) phase with strong dimer attraction and the staggered phase (SP) with strong dimer repulsion, there emerges a resonating plaquette (RP) phase with off-diagonal translational symmetry breaking. Such a quantum phase is separated from the LN via a first order transition and from the SP by the famous Rokhsar-Kivelson point. Our renormalization group analysis reveals the different flow directions, fully consistent with the order parameter histogram in Monte Carlo simulations. The realization and implication of our phase diagram in Rydberg experiments are proposed.
We study numerically spinless fermions with strong nearest-neighbor repulsion VVV on frustrated lattice structures that show macroscopically many ground states in the absence of a kinetic energy term (hopping term). A finite hopping amplitude ttt lifts the macroscopic degeneracy and leads to a small number of degenerate ground states. These can be characterized by topological quantum numbers and transformation properties under symmetry operations such as particle-hole interchange. Results for the criss-crossed checkerboard lattice (two-dimensional pyrochlore lattice) with up to 32 fermions support the scenario that translational invariance is restored in the thermodynamic limit, making half-charged quasiparticles possible. A finite entropy of approximately (3∕4)ln(4∕3)(3∕4)\mathrm{ln}(4∕3)(3∕4)ln(4∕3) per site is released at low temperatures ${k}_{B}T\ensuremath{\approx}{t}^{3}∕{V}^{2}$, much below the bare energies t,Vt,Vt,V. This is familiar from the widely studied models involving spins on frustrated lattices, but in a spinless-fermion model these low-energy excitations are necessarily related to charge degrees of freedom.