Abstract
Frustration is an important phenomenon in condensed matter physics because it can introduce a new order parameter such as chirality. Towards understanding a mechanism of the frustration in strongly correlated systems, we study a holographic superconductor model with three scalar fields and an interband Josephson coupling, which is important for the frustration. We analyze free energy of solutions of the model to determine ground states. We find chiral ground states, which have nonzero chirality.
Highlights
JHEP08(2015)136 help to understand a mechanism of the frustration in strongly correlated systems from the viewpoint of the gauge/gravity correspondence
We have analyzed the holographic superconductor model with some scalar fields and the Josephson coupling from the view point of gauge/gravity correspondence
We have seen that the frustration does not occur in the holographic two-scalar model because there is one Josephson coupling term only
Summary
We study a two-scalar model as a minimal model with the Josephson coupling. From the equations of motion of θi, we obtain θ1 − θ2 = 0 or π This solution is not frustrated because it minimizes the coefficient of the Josephson coupling potential term 2 cos (θ1 − θ2) in (2.3). ∇μF μν − 2ψ12Aν − 2ψ22Aν = 0, ∇μ∇μψ1 − AμAμψ1 − λ1ψ1 = 0, ∇μ∇μψ2 − AμAμψ2 − λ2ψ2 = 0 These equations of motion are same as those of a two-scalar model without the Josephson coupling. (2.23) and (2.24) are same as the equations of motion of a one-scalar model [5] It is well-known that the solution with ψ1 = 0 exists if the Hawking temperature of the black hole is low enough. If | | is large enough, λ1 is below Breitenlohner-Freedman bound [28] and the theory is unstable
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