Holographic subregion complexity of a (1+1)-dimensional $p$-wave superconductor

Fujita, Mitsutoshi

doi:10.1093/ptep/ptz058

Cited by 8 publications

(9 citation statements)

References 100 publications

(149 reference statements)

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“…Our results are in agreement with that reported in [44] and in [45] where the authors have studied 1 + 1-dimensionsal s-wave and p-wave holographic superconductor respectively: the complexity remains finite during the phase transition 3 and the subregion complexity plot leads to the same transition temperature as observed from the entropy plot. Ref.…”

Section: Discussionsupporting

confidence: 92%

“…Ref. [45] has also observed multivaluedness and discontinuous but finite jump in the complexity during the first order phase transition.…”

Section: Discussionmentioning

confidence: 93%

“…During the second order phase transition the complexity of the superconducting phase is opposite to what they have found. 45 There are multiple questions which need to be answered. It has been reported that the complexity decreases with increasing temperature during the second order phase transition, but in this paper we actually found that it behaves quite similar to that of the entropy for the superconducting phase.…”

Section: Discussionmentioning

confidence: 99%

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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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Section: Discussionsupporting

confidence: 92%

“…Ref. [45] has also observed multivaluedness and discontinuous but finite jump in the complexity during the first order phase transition.…”

Section: Discussionmentioning

confidence: 93%

Section: Discussionmentioning

confidence: 99%

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

Chakraborty

2020

Class. Quantum Grav.

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“…Initially, the holographic entanglement entropy and the holographic complexity are obtained for a strip in our model [21]- [33], [35,36]. In order to use the Poincare coordinates we choose a time slice in the metric (13) and replace the coordinate r by 1 ξ .…”

Section: Topological Invariants and The Critical Pointsmentioning

confidence: 99%

“…Also, it has been suggested that holographic subregion complexity (RT volume) can be used as a useful tool for probing superconductor phase transitions. Therefore, both holographic entanglement entropy and holographic subregion complexity are useful quantities to identify superconductor phase transitions [35,36,37,38].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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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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Holographic subregion complexity in general Vaidya geometry

Ling¹,

Liu²,

Niu³

et al. 2019

J. High Energ. Phys.

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We investigate general features of the evolution of holographic subregion complexity (HSC) on Vaidya-AdS metric with a general form. The spacetime is dual to a sudden quench process in quantum system and HSC is a measure of the "difference" between two mixed states. Based on the subregion CV (Complexity equals Volume) conjecture and in the large size limit, we extract out three distinct stages during the evolution of HSC: the stage of linear growth at the early time, the stage of linear growth with a slightly small rate during the intermediate time and the stage of linear decrease at the late time. The growth rates of the first two stages are compared with the Lloyd bound. We find that with some choices of certain parameter, the Lloyd bound is always saturated at the early time, while at the intermediate stage, the growth rate is always less than the Lloyd bound. Moreover, the fact that the behavior of CV conjecture and its version of the subregion in Vaidya spacetime implies that they are different even in the large size limit. * lingy@ihep.ac.cn

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Holographic subregion complexity of a (1+1)-dimensional $p$-wave superconductor

Cited by 8 publications

References 100 publications

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

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

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

Holographic subregion complexity in general Vaidya geometry

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