Nature of the kagome S=1/2 Heisenberg antiferromagnet quantum spin liquid

Determine whether the quantum spin liquid ground state of the spin-1/2 Heisenberg antiferromagnet on the kagome lattice is gapped or gapless, and establish whether its emergent gauge structure is U(1) or Z2.

Background

The kagome lattice with spin-1/2 Heisenberg antiferromagnetic interactions is a paradigmatic setting for strong geometric frustration and quantum fluctuations, making it a central candidate for hosting a quantum spin liquid. Despite extensive theoretical efforts using exact diagonalization, density matrix renormalization group, variational Monte Carlo, tensor networks, and functional renormalization, consensus has not been reached on the fundamental character of the ground state.

Conflicting results include reports of gapped and gapless phases, chiral gapped states, and gapless Dirac states with different gauge structures (U(1) versus Z2). This paper studies the MOF kagome material Cu3(HOTP)2 and finds its experimental behavior consistent with a gapless QSL, but the broader theoretical classification problem for the ideal kagome Heisenberg model remains unresolved as stated in the introduction.