FRG analysis of Z_n-anisotropic Gross-Neveu-Yukawa theories shows irrelevant anisotropy for n>3 yielding N=2 supersymmetric criticality and a second length scale whose exponent satisfies ν'/ν = 1 + |y_n|/2.
Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy
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abstract
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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Supersymmetric quantum criticality with discrete symmetry
FRG analysis of Z_n-anisotropic Gross-Neveu-Yukawa theories shows irrelevant anisotropy for n>3 yielding N=2 supersymmetric criticality and a second length scale whose exponent satisfies ν'/ν = 1 + |y_n|/2.