TY - JOUR

T1 - Ergodic Archimedean dimers

AU - Røising, Henrik Schou

AU - Zhang, Zhao

PY - 2023/8/11

Y1 - 2023/8/11

N2 - 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 com- patible 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.

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 com- patible 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.

U2 - 10.21468/SciPostPhysCore.6.3.054

DO - 10.21468/SciPostPhysCore.6.3.054

M3 - Journal article

VL - 6

JO - SciPost Physics Core

JF - SciPost Physics Core

SN - 2666-9366

IS - 3

M1 - 054

ER -