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

TL;DR

This paper shows that the effective theory for a 2+1D deconfined quantum critical point includes a Faddeev-Skyrme model component, leading to logarithmic violations of scaling due to emergent gauge symmetry.

Contribution

It reveals the role of the Faddeev-Skyrme term in the effective theory and its connection to logarithmic scaling violations at the quantum critical point.

Findings

Logarithmic correction to spin stiffness near criticality

Emergent gauge symmetry explains scaling violations

Faddeev-Skyrme model captures critical behavior

Abstract

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.