Deconfined quantum criticality and Néel order via dimer disorder

Recent results on the nature of the quantum critical point between Néel and valence bond solid (VBS) ordered phases of two-dimensional quantum magnets are examined by an attack from the VBS side. This approach leads to an appealingly simple physical description, and further insight into the properties of the transition.

Figure 1

(Color online) Schematic picture of the four degenerate ground states associated with the columnar VBS state. The encircled lines represent the bonds across which the spins are paired into a valence bond. The four ground states are associated with four different orientations of a $Z_4$ clock order parameter.

Figure 2

(Color online) An example of an elementary domain wall in the VBS state across which the clock angle shifts by $\pi ∕2$.

Figure 3

(Color online) Macroscopic picture of a $Z_4$ vortex as a point where four oriented elementary domain walls meet and end.

Figure 4

(Color online) The $Z_4$ vortex in the columnar VBS state. The blue lines represent the four elementary domain walls. At the core of the vortex there is an unpaired site with a free spin-$1∕2$ moment.

Figure 5

(Color online) The structure of the $Z_4$ vortex close to the transition. As one approaches the critical point, the domain walls (depicted as a blue-shaded region) become thicker. At the same time, the vortex core where the spin-$1∕2$ moment resides (depicted as a gray circular region) becomes larger. The domain wall thickness ${\xi }_{\mathit{VBS}}$ and the vortex core size $\xi$ both diverge at the transition but because the clock anistropy is irrelevant, the former diverges faster. Therefore, at intermediate length scales (larger than $\xi$ but smaller than ${\xi }_{\mathit{VBS}}$) the clock angle winds smoothly as in a regular $XY$ vortex.