Competing holographic orders

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.

Competition/enhancement of two probe order parameters in the unbalanced holographic superconductor

“…Contrarily to the general weak-coupling expectation, multiple orderings at strong coupling can coexist and even enhance one another. We observed the possibility of such an enhancement and, relying on a probe analysis, we found results in accordance with the conjecture advanced in [9] claiming that an attractive/repulsive interaction between the dual bulk fields leads to competition/enhancement of the corresponding order parameters. Our model possesses two charge densities associated to two Abelian symmetries U (1) A , U (1) B ; working in the canonical ensemble we studied the coexistence of two orderings both in an unbalanced (ρ A = ρ B ) and in a balanced (ρ A = ρ B ) setting.…”

“…Without pretending to be particularly close to any specific realistic model, let us however observe that the "magnetic" degrees of freedom giving rise to a condensate resemble itinerant ferromagnetism. Said otherwise, the degrees of freedom that we describe in terms of the "magnetic" condensate are not localized or fixed to any spatial pattern or lattice; in this respect, recall that our ansatz does not present any specific spatial features, neither periodicity nor lattice-like structures 9 . A condensate is likely to describe a plasma of degrees of freedom rather than an array of localized spins; this can be thought of in analogy with the fact that ψ is interpreted as a condensate of (clearly itinerant) Cooper-like pairs at strong coupling.…”

“…This is intuitively due to the fact that when the Fermi liquid undergoes an instability, a mass gap is usually produced. Such mass gap tends to prevent, or at least discourage, further instabilities [9].…”

“…In [9] it was conjectured that two holographic orders are competing or mutually enhancing when their interaction is respectively attractive or repulsive. The present model offers then a neat example where this conjecture is confirmed.…”

Chiral ground states in a frustrated holographic superconductor

“…From a viewpoint of the gauge/gravity correspondence [6][7][8], holographic superconductor models with several order parameters are well-studied [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In particular, a two-scalar model with the Josephson coupling was studied in ref.…”