Emergent quasi-one-dimensionality in a kagome magnet: A simple route to complexity

We study the ground-state phase diagram of the quantum spin-1/2 Heisenberg model on the kagome lattice with first-(J(1) < 0), second-(J(2) < 0), and third-neighbor interactions (J(d) > 0) by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the J(d)-dominant regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions J(1,2). When either J(1) or J(2) is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime J(1) similar or equal to J(2), a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.