Magnetic ground state of the 2D Wigner crystal near melting
In plain words
Electrons in the crystal can swap places by quantum tunneling, which couples their spins. Which spin arrangement results near the melting density, possibly a spin liquid (a state with no magnetic order even at zero temperature), is unknown.
Precise statement
For the triangular 2D Wigner crystal at r_s_c < r_s < ~100, the spin Hamiltonian is a ring-exchange model with competing two-, three-, four-, five- and six-particle exchange constants $J_k(r_s)$. Determine its ground state (ferromagnet, 120-degree antiferromagnet, or spin liquid) versus $r_s$, including the effect of screening by nearby gates.
What would settle it
Path-integral Monte Carlo exchange constants with error bars used in large-scale numerics (DMRG or tensor networks) of the ring-exchange model, or a measurement of the spin susceptibility of an imaged Wigner crystal.