Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy.
We study the three-dimensional XY model with a Zq anisotropic term. At temperatures T<Tc this dangerously irrelevant perturbation is relevant only above a length scale Lambda, which diverges as a power of the correlation length, Lambda approximately xi aq. Below Lambda the order parameter is U(1) symmetric. We derive the full scaling function controlling the emergence of U(1) symmetry and use Monte Carlo results to extract the exponent aq for q=4,...,8. We find that aq approximately a4(q/4)2, with a4 only marginally larger than 1. We discuss these results in the context of U(1) symmetry at deconfined quantum-critical points separating antiferromagnetic and valence-bond-solid states in quantum spin systems.
Lou
Jie
J
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.
Sandvik
Anders W
AW
Balents
Leon
L