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arXiv · 1905.01632

Topological invariants of the Ryu-Takayanagi ($RT$) surface used to observe holographic superconductor phase transition

Fatemeh Lalehgani Dezaki·Behrouz Mirza·Marzieh Moradzadeh·Zeinab Sherkatghanad
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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.

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Fatemeh Lalehgani Dezaki, Behrouz Mirza, Marzieh Moradzadeh, Zeinab Sherkatghanad. 2019-05-31. Topological invariants of the Ryu-Takayanagi ($RT$) surface used to observe holographic superconductor phase transition. https://doi.org/10.1016/j.nuclphysb.2019.114647

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