Quantum phase transitions in a bidimensional $O(N) \times {\mathbb{Z}_2}$ scalar field model

TL;DR

This paper investigates quantum phase transitions in a two-dimensional $O(N) imes bZ_2$ scalar field model, revealing how coupling strength and interaction sign influence transition types and conformality, with implications for cold atom systems.

Contribution

It provides a detailed analysis of phase transition patterns in a coupled scalar field model, highlighting the role of coupling and interaction sign in transition order and conformality constraints.

Findings

Second-order phase transition in strong coupling regime.

Finite mass gap in $O(N)$ sector prevents conformality.

Interaction sign significantly alters transition patterns.

Abstract

We analyze the possible quantum phase transition patterns occurring within the $O(N) \times {\mathbb{Z}_2}$ scalar multi-field model at vanishing temperatures in $(1+1)$-dimensions. The physical masses associated with the two coupled scalar sectors are evaluated using the loop approximation up to second order. We observe that in the strong coupling regime, the breaking $O(N) \times {\mathbb{Z}_2} \to O(N)$, which is allowed by the Mermin-Wagner-Hohenberg-Coleman theorem, can take place through a second-order phase transition. In order to satisfy this no-go theorem, the $O(N)$ sector must have a finite mass gap for all coupling values, such that conformality is never attained, in opposition to what happens in the simpler ${\mathbb{Z}_2}$ version. Our evaluations also show that the sign of the interaction between the two different fields alters the transition pattern in a significant way. These results may be relevant to describe the quantum phase transitions taking place in cold linear systems with competing order parameters. At the same time the super-renormalizable model proposed here can turn out to be useful as a prototype to test resummation techniques as well as non-perturbative methods.