Fig. 1: Spin-Peierls distortions of unstable gapless spin liquids in one and two dimensions.
From: Spin-Peierls instability of the U(1) Dirac spin liquid
a In one dimension, the spin-half antiferromagnetic Heisenberg chain is unstable to dimerisation when coupled to the lattice. The U(1) Dirac spin liquid is unstable to \(\sqrt{12}\times\! \sqrt{12}\) and pinwheel valence-bond order on the b triangular and c kagome lattices, respectively. The blue shifted dots show the distorted lattice, the vector displacements inside the unit cell u(r) are highlighted by white arrows. The enhanced nearest-neighbour bond strengths within each plaquette are depicted in the left panel, and the short-range spin-spin correlations \(\langle \vec{S}\cdot \vec{S}\rangle\) are shown on the right. Structural transitions can be measured thermodynamically, and the corresponding lattice and valence-bond order can be measured with inelastic X-ray and neutron spectroscopy.
