Abstract
We study the phase transitions in the metal/superconductor system using topological invariants of the Ryu-Takayanagi (RT) surface and the volume enclosed by the RT surface in the Lifshitz black hole background. It is shown that these topological invariant quantities identify not only the phase transition but also its order. According to these findings a discontinuity slope is observed at the critical points for these invariant quantities that correspond to the second order of phase transition. These topological invariants provide a clearer illustration of the superconductor phase transition than do the holographic entanglement entropy and the holographic complexity. Also, the backreaction parameter, k, is found to have an important role in distinguishing the critical points. The reducing values of the parameter k means that the backreaction of the matter fields are negligible. A continuous slope is observed around the critical points which is characteristic of the probe limit. In addition, exploring the nonlinear electrodynamic, the effects of the nonlinear parameter, β, is investigated. Finally the properties of conductivity are numerically explored in our model.
Highlights
To describe theories with strong coupling constants, one can use the AdS/CFT duality according to which, the physics of the conformal field theory (CFT) on the boundary of the AdS space time can be related to a gravitational theory in the bulk [1, 2, 3]
We considered a Lifshitz black hole background and a nonlinear electrodynamic to investigate the holographic metal/superconductor phase transition using the topological invariants of the RT surface
We explored the superconductor phase transition by calculating the holographic entanglement entropy and holographic subregion complexity in our model
Summary
To describe theories with strong coupling constants, one can use the AdS/CFT duality according to which, the physics of the conformal field theory (CFT) on the boundary of the AdS space time can be related to a gravitational theory in the bulk [1, 2, 3]. The interpretation of these topological invariants in the dual field theory are not yet given and remain to be a challenge Plotting these invariant quantities as a function of temperature, a discontinuity slope is detected at critical points which specifies the second order of phase transition and shows the phase transition in the metal/superconductor system more clearly than the holographic entanglement entropy and holographic complexity do. These topological invariants are useful tools for probing the superconductor phase transition. We introduce other topological invariants of the RT surface and the volume enclosed by it and see how the critical point in the metal/superconductor system can be identified by these quantities
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