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Register a new userEntanglement Entropy as a Probe of the Proximity Effect in Holographic Superconductors
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Papantonopoulos Eleftherios
Publication date
2014
fields
Physics
and research's language is
English
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We study the entanglement entropy as a probe of the proximity effect of a superconducting system by using the gauge/gravity duality in a fully back-reacted gravity system. While the entanglement entropy in the superconducting phase is less than the entanglement entropy in the normal phase, we find that near the contact interface of the superconducting to normal phase the entanglement entropy has a different behavior due to the leakage of Cooper pairs to the normal phase. We verify this behavior by calculating the conductivity near the boundary interface.
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We study the behavior of holographic entanglement entropy (HEE) for imbalanced holographic superconductors. We employ a numerical approach to consider the robust case of fully back-reacted gravity system. The hairy black hole solution is found by using our numerical scheme. Then it is used to compute the HEE for the superconducting case. The cases we study show that in presence of a mismatch between two chemical potentials, below the critical temperature, superconducting phase has a lower HEE in comparison to the AdS-Reissner-Nordstrom black hole phase. Interestingly, the effects of chemical imbalance are different in the contexts of black hole and superconducting phases. For black hole, HEE increases with increasing imbalance parameter while it behaves oppositely for the superconducting phase. The implications of these results are discussed.
We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newtons constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.
In this paper, we will propose a universal relation between the holographic complexity (dual to a volume in AdS) and the holographic entanglement entropy (dual to an area in AdS). We will explicitly demonstrate that our conjuncture hold for all a metric asymptotic to AdS$_3$, and then argue that such a relation should hold in general due to the AdS version of the Cavalieri principle. We will demonstrate that it holds for Janus solution, which have been recently been obtained in type IIB string theory. We will also show that this conjecture holds for a circular disk. This conjecture will be used to show that the proposal that the complexity equals action, and the proposal that the complexity equal volume can represent the same physics. Thus, using this conjecture, we will show that the black holes are fastest computers, using the proposal that complexity equals volume.
We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the $T bar{T}$ deformation. Under the boost and $T bar{T}$ deformation, the $c$-function of the entanglement entropy exactly shows the features expected by the Zamoldchikovs $c$-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincare cutoff AdS space can reproduce the exact same result of the $T bar{T}$ deformed theory on a two-dimensional sphere.
The thermalization process of the holographic entanglement entropy (HEE) of an annular domain is investigated over the Vaidya-AdS geometry. We numerically determine the Hubeny-Rangamani-Takayanagi (HRT) surface which may be a hemi-torus or two disks, depending on the ratio of the inner radius to the outer radius of the annulus. More importantly, for some fixed ratio of two radii, it undergoes a phase transition or double phase transitions from a hemi-torus configuration to a two-disk configuration, or vice versa, during the thermalization. The occurrence of various phase transitions is determined by the ratio of two radii of the annulus. The rate of entanglement growth is also investigated during the thermal quench. The local maximal rate of entanglement growth occurs in the region with double phase transitions. Finally, if the quench process is fairly slow which may be controlled by the thickness of null shell, the region with double phase transitions vanishes.
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