Emergent quasi-one-dimensionality in a kagom\'e magnet: A simple route to complexity

TL;DR

This paper investigates the complex ground states of a frustrated kagome lattice quantum magnet using analytical and numerical methods, revealing a rich phase diagram with novel valence bond crystal phases and ruling out some previously proposed spin liquids.

Contribution

It provides the first comprehensive understanding of the phase diagram of a highly frustrated 2D quantum antiferromagnet with combined analytical and DMRG approaches.

Findings

Identification of cuboc1 and cuboc2 magnetic phases with non-coplanar order

Discovery of a valence bond crystal phase in the compensated regime

No evidence found for 1D gapless or chiral spin liquids

Abstract

We study the ground state phase diagram of the quantum spin-$1/2$ Heisenberg model on the kagom\'{e} 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 inter-chain interactions $J_{1,2}$. When either $J_1$ or $J_2$ is dominant, the model is found to support one of two cuboctohedral phases, cuboc1 and cuboc2. These cuboc states host non-coplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime $J_1 \simeq J_2$, 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 (2d) quantum antiferromagnet. We find no evidence of either the one-dimensional (1d) gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean field theories.