On the triplet of holographic phase transition

Abstract

We start from an Einstein − Maxwell system coupled with a charged scalar field in Anti−de Sitter space−time. In the setup where the pressure P is identified with the cosmological constant, the AdS black hole (BH) undergoes the phase transition from small to large BHs, which is similar to the transition from liquid to gas in the van der Waals theory. Based on this framework, we study the triplet of holographic superconducting states, consisting of ground state and two lowest excited states. Our numerical calculations show that the pressure variation in the bulk creates a mechanism in the boundary which causes changes in the physical properties of excited states, namely: a) when the pressure P is higher than the critical pressure P c (P > P c ) of the phase transition from small to large BHs the ground state and the first excited state are superconducting states while the second excited state is the normal one. However, at lower pressure, P ≤ P c , the ground state is solely the superconducting state. We conjecture that the precedent phenomena could take place when the scalar field in the bulk is replaced by other matter fields.

Asymptotic critical behavior of holographic superconductor phase transition — the spectrum of excited states becomes continuous at T = 0

“…This means that, at this chemical potential, the system goes through phase transition to the ground, 1st excited, and 2nd excite states at T c =1.699, 0.295, and 0.0806 respectively. These values exactly match critical temperatures obtained by directly solving the full system of equations of motion [17] (see also figure 1). Here, they are obtained through a much simpler method, by solving only one linear equation.…”

“…On the other hand, remarkably for the case L = 1 (the liquid side of the vdW BH transition), the gap between the 1st excited state and the ground state keeps shrinking. This might correlate with the fact that we do not see gap in the conductivity at low temperature for excited states in the gas side of the vdW transition [17]. In both cases, the ground state threshold µ 0 saturates at a finite, non-zero value.…”