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

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.

22 pages, 6 figures. Replaced with version matching the one published in the JHEP. Minimal changes

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