Density driven symmetry breaking and Butterfly effect in holographic superconductors

Understand

We study the density driven symmetry breaking in holographic superconductors by considering the positive mass squared case.

• We show that even for the positive $m^2$, a scalar condensation still forms, provided the chemical potential is high enough.
• As $m^2$ increases, the phase space folds due to the non-linearity of the equations of motion, and two nearby points in the phase space can represent symmetry breaking and preserving configurations respectively.
• The phase space defined by the set of initial conditions of field variables at the horizon undergoes a non-linear radial evolution to result in the phase space folding, a characteristic phenomenon in a non-linear system.