Holographic Entanglement Entropy in 2D Holographic Superconductor via $AdS_3/CFT_2$

TL;DR

This paper calculates the holographic entanglement entropy in 2D holographic superconductors using $AdS_3/CFT_2$, revealing linear behavior with belt angle, no confinement transition, and a phase transition near the critical point.

Contribution

It provides an exact and approximate analysis of HEE in 2D holographic superconductors, including numerical methods and phase transition insights.

Findings

HEE varies linearly with belt angle.

No confinement/deconfinement phase transition observed.

A first order phase transition occurs near the critical temperature.

Abstract

The aim of the present letter is to find the holographic entanglement entropy (HEE) in 2D holographic superconductors (HSC). Indeed, it is possible to compute the exact form of this entropy due to an advantage of approximate solutions inside normal and superconducting phases with backreactions. By making the UV and IR limits applied to the integrals, an approximate expression for HEE is obtained. In case the software cannot calculate minimal surface integrals analytically, it offers the possibility to proceed with a numerical evaluation of the corresponding terms. We'll understand how the area formula incorporates the structure of the domain wall approximation. We see that HEE changes linearly with belt angle. It's due to the extensivity of this type of entropy and the emergent of an entropic force. We find that the wider belt angle corresponds to a larger holographic surface. Another remarkable observation is that no "confinement/deconfinement" phase transition point exists in our $2D$ dual field theory. Furthermore we observe that the slope of the HEE with respect to the temperature freedom(s) in low temperature system. A first order phase transition is detected near the critical point.