Competing Valence Bond Crystals in the Kagome Quantum Dimer Model

TL;DR

This paper investigates competing valence bond crystal phases in the Kagome quantum dimer model, revealing a new 12-site resonating-columnar VBC alongside a known 36-site VBC, with implications for understanding the quantum spin liquid behavior.

Contribution

It introduces a non-perturbative analysis showing the coexistence of two distinct valence bond crystal phases in the Kagome quantum dimer model, highlighting their different topological sectors.

Findings

Identification of a 12-site resonating-columnar VBC

Coexistence with a 36-site VBC in different topological sectors

Large ground state degeneracy suggesting proximity to a Z_2 dimer liquid

Abstract

The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}" VBC. The exceptionally large degeneracy of the GS multiplets (144 on our 108-site cluster) might reflect the proximity of the Z_2 dimer liquid. Interestingly, these two VBC "emerge" in {\it different topological sectors}. Implications for the interpretation of numerical results on the QHAF are outlined.