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

Abstract

We study the ground state phase diagram of the quantum spin-$1/2$ Heisenberg model on the kagomé 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.

16 pages, 14 figures

References in corpus (16)

• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Identifying Topological Order by Entanglement Entropy
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet
• Spinons and triplons in spatially anisotropic frustrated antiferromagnets
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Toward Perfection: Kapellasite, Cu3Zn(OH)6Cl2, a New Model S = 1/2 Kagome Antiferromagnet
• Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
• Spin dynamics and disorder effects in the S=1/2 kagome Heisenberg spin liquid phase of kapellasite
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Classification and detection of symmetry fractionalization in chiral spin liquids

Cited by in corpus (17)

• Herbertsmithite and the Search for the Quantum Spin Liquid
• Possible Dirac quantum spin liquid in a kagome quantum antiferromagnet YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]
• Intertwined nematic orders in a frustrated ferromagnet
• Effect of Zn doping on the antiferromagnetism in kagome Cu${}_{4-x}$Zn${}_x$(OH)${}_6$FBr
• The magnetic Hamiltonian and phase diagram of the quantum spin liquid Ca10Cr7O28
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality
• From frustrated magnetism to spontaneous Chern insulators
• Degenerate and chiral states in the extended Heisenberg model in the kagome lattice
• Chiral Spin Order in Kondo-Heisenberg systems
• Magnetic phase diagram of Cu${}_{4-x}$Zn${}_x$(OH)${}_6$FBr studied by neutron-diffraction and $\mu$SR techniques
• Antiferromagnetism in kagome $\alpha$-Cu${}_3$Mg(OH)${}_6$Br${}_2$
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Striped Magnetic Ground State of the Kagome Lattice in Fe4Si2Sn7O16
• Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO${}_4$
• Competition between dimerization and vector chirality in the spin-$3/2$ $J_1$-$J_2$ Heisenberg chain with uniaxial single-ion anisotropy
• Robust semiclassical magnetization plateau in the kagome lattice