Competing Holographic Orders

TL;DR

This paper investigates how different macroscopic orders, such as superconducting and magnetic, compete or cooperate in a holographic framework, revealing that they generally tend to compete unless strong repulsive interactions are present.

Contribution

It introduces a holographic model for competing orders, analyzing the conditions under which they hinder or enhance each other, and provides both analytic and numerical insights.

Findings

Orders tend to compete in holographic models.

Strong repulsive interactions can enable coexistence.

Holographic orders generally compete unless interactions are repulsive.

Abstract

We model competition between different macroscopic orders in an holographic context. The orders we considered are a superconducting order, modeled by a charged scalar field, and a magnetic order modeled by a neutral scalar field. We also discuss the case of two competing scalars coupled to a single gauge field. In all cases discussed here the phases tend to compete, rather than enhance each other. The condensation of one scalar hinders any further instabilities, unless we have a sufficiently strong repulsive interactions between the bulk scalars. We provide both analytic arguments and numerical demonstration of this fact. Based on the cases discussed here, we conjecture that holographic orders tend to compete for attractive bulk interactions, including gravity, and to cooperate, or be mutually enhancing, for repulsive bulk interactions between the corresponding order parameters.