Holographic complexity of anisotropic black branes

Mansoori, Seyed Ali Hosseini; Jahnke, Viktor; Qaemmaqami, Mohammad M.; Olivas, Yaithd D.

doi:10.1103/physrevd.100.046014

Cited by 49 publications

(48 citation statements)

References 72 publications

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“…If we choose: f 0 = −R 2 f (z)e −χ(z) , f 1 = R 2 , f 2 = R 2 f (z) and d = 3, we arrive at our results (25)(26)(27)(28)(29).…”

Section: A the Subregion Complexity In (D+1)-dimensionsmentioning

confidence: 72%

On the complexity of a 2 + 1-dimensional holographic superconductor

Chakraborty

2020

Class. Quantum Grav.

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We present the results of our computation of the subregion complexity and also compare it with the entanglement entropy of a 2 + 1-dimensional holographic superconductor which has a fully backreacted gravity dual with a stable ground sate. We follow the "complexity equals volume" or the CV conjecture. We find that there is only a single divergence for a strip entangling surface and the complexity grows linearly with the large strip width. During the normal phase the complexity increases with decreasing temperature, but during the superconducting phase it behaves differently depending on the order of phase transition. We also show that the universal term is finite and the phase transition occurs at the same critical temperature as obtained previously from the free energy computation of the system. In one case, we observe multivaluedness in the complexity in the form of an "S" curve.

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“…If we choose: f 0 = −R 2 f (z)e −χ(z) , f 1 = R 2 , f 2 = R 2 f (z) and d = 3, we arrive at our results (25)(26)(27)(28)(29).…”

Section: A the Subregion Complexity In (D+1)-dimensionsmentioning

confidence: 72%

On the complexity of a 2 + 1-dimensional holographic superconductor

Chakraborty

2020

Class. Quantum Grav.

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“…It is noticed that here we computed the holographic complexity via complexity=volume conjecture and resolved its UV divergence tactfully. As is known that another independent proposal to evaluate the complexity is complexity=action conjecture [46,47,62]. Then an important question involved is whether the physical features we found depends on the chosen conjecture.…”

Section: Conclusion and Discussionmentioning

confidence: 96%

Holographic entanglement entropy and complexity in Stückelberg superconductor

2019

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The holographic superconductors, as one of the most important application of gauge/gravity duality, promote the study of strongly coupled superconductors via classical general relativity living in one higher dimension. One of the interesting properties in holographic superconductor is the appearance of first and second order phase transitions. Recently, another active studies in holographic framework is the holographic entanglement entropy and complexity evaluated from gravity side. In this note, we study the properties of the holographic entanglement entropy and complexity crossing both first and second order phase transitions in Stückelberg superconductor.We find that they behave differently in two types of phase transitions. We argue that holographic entanglement entropy and complexity conjectured with the volume can also be a possible probe to the type of superconducting phase transition.

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“…While the Lloyd's bound was first introduced in the study of the CA conjecture, recent studies [38,64,87,88] show that the CA conjecture violates the Lloyd's bound in many cases. It was for the first time reported by [38,64] independently that even in the late time limit the CA conjecture violates the the Lloyd's bound because it saturates to the bound from above.…”

Section: Discussionmentioning

confidence: 99%

Complexity of holographic superconductors

Yang

Jeong

Niu

et al. 2019

J. High Energ. Phys.

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We study the complexity of holographic superconductors (Einstein-Maxwellcomplex scalar actions in d + 1 dimension) by the "complexity = volume" (CV) conjecture. First, it seems that there is a universal property: the superconducting phase always has a smaller complexity than the unstable normal phase below the critical temperature, which is similar to a free energy. We investigate the temperature dependence of the complexity. In the low temperature limit, the complexity (of formation) scales as T α , where α is a function of the complex scalar mass m 2 , the U (1) charge q, and dimension d. In particular, for m 2 = 0, we find α = d−1, independent of q, which can be explained by the near horizon geometry of the low temperature holographic superconductor. Next, we develop a general numerical method to compute the time-dependent complexity by the CV conjecture. By this method, we compute the time-dependent complexity of holographic superconductors. In both normal and superconducting phase, the complexity increases as time goes on and the growth rate saturates to a temperature dependent constant. The higher the temperature is, the bigger the growth rate is. However, the growth rates do not violate the Lloyd's bound in all cases and saturate the Lloyd's bound in the high temperature limit at a late time.

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Holographic complexity of anisotropic black branes

Cited by 49 publications

References 72 publications

On the complexity of a 2 + 1-dimensional holographic superconductor

On the complexity of a 2 + 1-dimensional holographic superconductor

Holographic entanglement entropy and complexity in Stückelberg superconductor

Complexity of holographic superconductors

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