Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy

Details Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy

2007-04-11

arxiv.org/abs/0704.1472v2

Phys. Rev. Lett. 99, 207203 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 4 figures. v2: co-author added, exact scaling function derived

Scientific paper

10.1103/PhysRevLett.99.207203

We study the three-dimensional XY model with a Z_q 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 ~ xi^a_q. 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 a_q for q=4,...,8. We find that a_q = a_4 (q/4)^2, with a_4 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.

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