Ground-state phase of the kagome Heisenberg model
Determine the thermodynamic ground-state phase and excitation gap of for spin on the uniform kagome lattice, with nearest-neighbor antiferromagnetic coupling one and no additional interactions.
Problem statement
Determine the thermodynamic ground-state phase and excitation gap of for spin on the uniform kagome lattice, with nearest-neighbor antiferromagnetic coupling one and no additional interactions.
Lean 4
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Background
This concrete frustrated quantum magnet is a canonical spin-liquid benchmark. Competing interpretations include a gapped spin liquid and a gapless Dirac spin liquid; the 2026 primary numerical study cited below describes the continuing dispute.
The target requires controlled thermodynamic extrapolation, certified numerical bounds or a proof. Finite-cylinder spectra, variational energies and finite bond dimensions are evidence with limitations, not an exact phase determination. Magnetic materials with further-neighbor or anisotropic interactions, square-kagome models and breathing-kagome variants are different Hamiltonians.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
numerical: A published 2026 study examines competing kagome spin-liquid descriptions; the full thermodynamic phase remains unresolved. Evidence
- [1]Jiang et al., kagome spin-liquid study, npj Computational Materials (2026) link
Recorded progress
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