Deconfined Quantum Criticality and Conformal Phase Transition in Two-Dimensional Antiferromagnets

Abstract

Deconfined quantum criticality of two-dimensional $SU(2)$ quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP${}^1$ model with a Maxwell term in 2+1 spacetime dimensions. We introduce a new perspective on deconfined quantum criticality within a field-theoretic framework based on an expansion in powers of $\epsilon =4-d$ for fixed number $N$ of complex matter fields. We show that in the allegedly weak first-order transition regime, a so-called conformal phase transition leads to a genuine deconfined quantum critical point. In such a transition, the gap vanishes when the critical point is approached from above and diverges when it is approached from below. We also find that the spin stiffness has a universal jump at the critical point.

v2: 6 two-column pages, 2 figures; published version; this version includes finite-size scaling arguments and discussion of the Néel susceptibility; references added

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