Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations

Abstract

We develop a new functional renormalization group (FRG) approach for the two-dimensional XY-model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)] with a duality transformation which explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include weak amplitude as well as out-of-plane fluctuations of the spins, which lead to additional interactions between the vortices that do not spoil the Berezinskii-Kosterlitz-Thouless transition. This demonstrates that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.

23 pages, 5 figures; minor changes

References in corpus (5)

• Exact evolution equation for the effective potential
• Vortex proliferation in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional lattice of Bose-Einstein condensates
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Connecting Berezinskii-Kosterlitz-Thouless and BEC phase transitions by tuning interactions in a trapped gas
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition

Cited by in corpus (4)

• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization