Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet

TL;DR

This paper introduces a non-perturbative method to map low-energy frustrated Heisenberg antiferromagnets to effective Quantum Dimer Models, providing insights especially into the kagome antiferromagnet's properties.

Contribution

It develops a formal, lattice-independent framework for deriving effective Hamiltonians and applies it to the kagome antiferromagnet, capturing its essential physics.

Findings

Effective Hamiltonian for kagome antiferromagnet derived

Method captures key properties of the microscopic model

Provides a deep understanding of low-energy excitations

Abstract

We propose a general non-perturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective Generalized Quantum Dimer Models. We develop the formal lattice independent frame and establish some important results on (i) the locality of the generated Hamiltonians (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian - shown to capture the essential properties and provide deep insights on the microscopic model [D. Poilblanc, M. Mambrini and D. Schwandt, arXiv:0912.0724] - is derived.