The image shown on the main page is from the paper Propagation of Disturbances in Degenerate Quantum Systems, it demonstrates that by placing a local magnetic field on a periodic J1-J2 Heisenberg spin chain at the Majumdar-Ghosh point (J2=.5*J1) a disturbance can be sent throughout the entire chain by changing the size of the boundary between the spins in the field and those not in the field. With no field applied the ground-state is degenerate, and the ground-state manifold is the manifold spanned by the two ways the system can be covered by singlets.

The figure at the top right shows a map of the two-point entanglement of the system (brighter is more entanglement, darker is less) at a lower field value, in this picture one can see that the two-point entanglement of the spins within the field is still very much like a singlet, and that there is a boundary between the field and non-field are roughly for spins long (white square shows where the field is applied). The figure at the bottom right shows the two-point entanglement of the system at a higher field, where you can see that all traces of a singlet have been destroyed within the section of the chain where the field is applied, and the boundary between the field and non-field region is roughly 3 spins long. Notice that the singlet covering switches for the spins far from the local field, this means that in a process connecting these two regions of phase space a disturbance has been sent throughout the system.

The 2 figures on the right show trace distances for the ground state of different total spin sectors. The top right figure shows trace distance from the nearest singlet covering for the 2 furthest spins from the field. The bottom right figure shows instead the trace distance from the nearest state in the entire ground state manifold. These plots clearly show abrupt transitions in the singlet covering. Note that at zero field the L=0 sector contains the global ground state, but this switches by a true crossing in such a way that the global ground state far from the field spins always is very close to one of the singlet coverings.