# Nonperturbative renormalization group treatment of amplitude fluctuations for $|\varphi|^4$ topological phase transitions

## TL;DR

This paper develops a nonperturbative renormalization group method in amplitude-phase representation to analyze topological phase transitions in $| ext{phi}|^4$ models, accurately capturing fixed points and thermodynamics.

## Contribution

It introduces a novel functional renormalization group scheme in AP representation, effectively handling amplitude fluctuations and unifying lattice XY and continuum $| ext{phi}|^4$ models.

## Key findings

- Correctly reproduces fixed point line and universal thermodynamics.
- Provides estimates for universal and nonuniversal quantities matching Monte Carlo results.
- Flexible approach applicable to experimentally relevant parameter ranges.

## Abstract

The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional $|\varphi|^4$ models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is a natural way to study the contribution of density fluctuations to nonuniversal quantities. We introduce a functional renormalization group scheme in AP representation where amplitude fluctuations are integrated first to yield an effective sine-Gordon model with renormalized superfluid stiffness. By a mapping between the lattice XY and continuum $|\varphi|^4$ models, our method applies to both on equal footing. Our approach correctly reproduces the existence of a line of fixed points and of universal thermodynamics and it allows to estimate universal and nonuniversal quantities of the two models, finding good agreement with available Monte Carlo results. The presented approach is flexible enough to treat parameter ranges of experimental relevance.