Deconfined quantum criticality and logarithmic violations of scaling from emergent gauge symmetry

We demonstrate that the low-energy effective theory for a deconfined quantum critical point in $d=2+1$ dimensions contains a leading-order contribution given by the Faddeev-Skyrme model. The Faddeev-Skyrme term is shown to give rise to the crucial Maxwell term in the CP${}^1$ field theory governing the deconfined quantum critical point. We derive the leading contribution to the spin stiffness near the quantum critical point and show that it exhibits a logarithmic correction to scaling of the same type as recently observed numerically in low-dimensional models of quantum spin systems featuring a quantum critical point separating an antiferromagnetically ordered state from a valence bond solid state. These corrections, appearing away from upper or lower critical dimensions, reflect an emergent gauge symmetry of low-dimensional antiferromagnetic quantum spin systems.

Figure 1

Schematic flow diagram of the $C{P}^1$ model with a compact Maxwell term. The Maxwell term allows for an interpolation between the $\text{O}\left(3\right)$ and $\text{O}\left(4\right)$ nonlinear $\sigma$ model fixed points.