TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.3.054
TI  - Ergodic Archimedean dimers
PY  - 2023/08/11
UR  - https://www.scipost.org/SciPostPhysCore.6.3.054
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 3
SP  - 054
A1  - Røising, Henrik Schou
AU  - Zhang, Zhao
AB  - We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.
ER  -

@Article{10.21468/SciPostPhysCore.6.3.054,
	title={{Ergodic Archimedean dimers}},
	author={Henrik Schou Røising and Zhao Zhang},
	journal={SciPost Phys. Core},
	volume={6},
	pages={054},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.3.054},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.3.054},
}