Classical correlations of defects in lattices with geometrical frustration in the motion of a particle

Abstract

We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied analytically and numerically. We consider different coverings for four different lattices: square, honeycomb, triangular, and diamond. In the case of hard-core dimer covering, we verify the existed results for the square and triangular lattice and obtain new ones for the honeycomb and the diamond lattices while in the case of loop covering we obtain new numerical results for all the lattices and use the existing analytical Liouville field theory for the case of square lattice.The results show power-law correlations for the square and honeycomb lattice, while exponential decay with distance is found for the triangular and exponential decay with the inverse distance on the diamond lattice. We relate this fact with the lack of bipartiteness of the triangular lattice and in the latter case with the three-dimensionality of the diamond. The connection of our findings to the problem of fractionalized charge in such lattices is pointed out.

arXiv comment6 pages, 6 figures, 1 table

References in corpus (13)

• An RVB phase in the triangular lattice quantum dimer model
• Quantum Monte Carlo with Directed Loops
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Dipolar spin correlations in classical pyrochlore magnets
• Enhanced magnetocaloric effect in frustrated magnets
• Coulomb and Liquid Dimer Models in Three Dimensions
• Classical dimers on the triangular lattice
• Field theory of compact polymers on the square lattice
• Fractional charges in pyrochlore lattices
• Pocket Monte Carlo algorithm for classical doped dimer models
• Planar pyrochlore, quantum ice and sliding ice
• Conformational Entropy of Compact Polymers

Cited by in corpus (5)

• Optical Kagome lattice for ultra-cold atoms with nearest neighbor interactions
• Correlated Fermions on a Checkerboard Lattice
• Fermionic quantum dimer and fully-packed loop models on the square lattice
• $Z_3$ topological order in the quantum dimer-pentamer model
• Fractionally charged excitations on frustrated lattices