Relativistic BEC extracted from a complex FRG flow equation

TL;DR

This paper employs the functional renormalization group to analyze relativistic Bose-Einstein condensation, revealing how quantum fluctuations influence phase diagrams beyond mean field approximations.

Contribution

It introduces a complex flow equation for the effective potential in relativistic BEC within the FRG framework, highlighting the impact of quantum fluctuations on phase transitions.

Findings

FRG-derived phase diagrams deviate from mean field results, especially in strongly coupled regimes.

Quantum fluctuations significantly affect the nonperturbative formation of BEC.

The complex effective potential approach enables analysis of relativistic BEC with the Litim regulator.

Abstract

Based on the functional renormalization group (FRG) under the local potential approximation, we analyze the Bose-Einstein condensation (BEC) in the relativistic complex scalar theory. This framework leads to a complex flow equation of the effective potential, even with the well-known Litim regulator. In order to evaluate the condensate from such a complex effective potential, we impose a condition between chemical potential and mass, analogously to those in the free theory or the mean field theory. We elucidate that for the strongly (weakly) coupled theory, the phase diagrams computed from the FRG are more (less) deviated from that under the mean field approximation. This result implies that quantum fluctuations strongly affect the nonperturbative formation of the BEC.