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.

References

The theoretical QSL ground state of the S=1/2 Heisenberg AF model on the kagome lattice is still far from clear, despite numerous investigations. Some key questions are whether it is gapped or gapless and whether it has U(1) or Z$_2$ gauge structure.

— Spin liquid properties of the kagome material Cu$_3$(HOTP)$_2$  (2411.18518 - Pratt et al., 2024) in Introduction, Section 1

Here, we refrain from drawing conclusions about whether the KSL phase is gapped or gapless, as our results are only obtained from finite-size YC6 simulations, and determining the nature of the KSL in the two-dimensional limit is beyond the scope of the present work.

— Unraveling the Kagome Antiferromagnetic $3J$ Model and Its Materials: An Integrated Approach  (2609.11745 - Lu et al., 10 Sep 2026) in Supplemental Material, Section I, paragraph following Fig. SMSpin

On the experimental side, we note that our thermal measurements have not yet accessed a sufficiently low-temperature regime to resolve the $T2$ specific heat ($C_v \propto T2$) expected for a Dirac QSL. Accessing this regime numerically will require further advances in finite-temperature numerical methods to enable reliable simulations at lower temperatures.

— Unraveling the Kagome Antiferromagnetic $3J$ Model and Its Materials: An Integrated Approach  (2609.11745 - Lu et al., 10 Sep 2026) in Summary and Discussion