Quantum dimer model for the spin-1/2 kagome Z2 spin liquid

Abstract

We revisit the description of the low-energy singlet sector of the spin-1/2 Heisenberg antiferromagnet on kagome in terms of an effective quantum dimer model. With the help of exact diagonalizations of appropriate finite-size clusters, we show that the embedding of a given process in its kagome environment leads to dramatic modifications of the amplitudes of the elementary loop processes, an effect not accessible to the standard approach based on the truncation of the Hamiltonian to the nearest-neighbour valence-bond basis. The resulting parameters are consistent with a Z${}_2$ spin liquid rather than with a valence-bond crystal, in agreement with the last density matrix renormalization group results.

Potential terms of the effective QDM included

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• Quantum spin liquid in the semiclassical regime
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
• From the $SU(2)$ Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagomé Lattice: Phase Transition and Fractionalized Flux Strings
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• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
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• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
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