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Register a new userEntanglement Entropy in Holographic P-Wave Superconductor/Insulator Model
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We continue our study of entanglement entropy in the holographic superconducting phase transitions. In this paper we consider the holographic p-wave superconductor/insulator model, where as the back reaction increases, the transition is changed from second order to first order. We find that unlike the s-wave case, there is no additional first order transition in the superconducting phase. We calculate the entanglement entropy for two strip geometries. One is parallel to the super current, and the other is orthogonal to the super current. In both cases, we find that the entanglement entropy monotonically increases with respect to the chemical potential.
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We examine the behavior of entanglement entropy of a subsystem $A$ in a fully backreacted holographic model of a $1+1$ dimensional $p$ wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size $l$ smaller than a critical size $l_{c1}$, entanglement entropy continues to increase as a function of the charge density as we cross the phase transition. When $l$ lies between $l_{c1}$ and another critical size $l_{c2}$ the entanglement entropy displays a non-monotonic behavior, while for $l > l_{c2}$ it decreases monotonically. At large charge densities entanglement entropy appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.
We investigate holographic cosmologies appearing in the braneworld model with a uniformly distributed $p$-brane gas. When $p$-branes extend to the radial direction, an observer living in the brane detects $(p-1)$-dimensional extended objects. On this background, we show that the braneworld model reproduces the expanding universes of the standard cosmology. In an expanding universe with a matter, we investigate the entanglement entropy between the visible and invisible universes across the cosmological (or particle) horizon. We show that, though the visible and invisible universes are causally disconnected, the nonlocal quantum correlation gives rise to a nontrivial time-dependent entanglement entropy relying on the matter.
We study the Kibble-Zurek mechanism in a 2d holographic p-wave superconductor model with a homogeneous source quench on the critical point. We derive, on general grounds, the scaling of the Kibble-Zurek time, which marks breaking-down of adiabaticity. It is expressed in terms of four critical exponents, including three static and one dynamical exponents. Via explicit calculations within a holographic model, we confirm the scaling of the Kibble-Zurek time and obtain the scaling functions in the quench process. We find the results are formally similar to a homogeneous quench in a higher dimensional holographic s-wave superconductor. The similarity is due to the special type of quench we take. We expect differences in the quench dynamics if the condition of homogeneous source and dominance of critical mode are relaxed.
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 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.
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