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

Abstract

We analyze the holographic subregion complexity in a $3d$ black hole with the vector hair. This $3d$ black hole is dual to a $1+1$ dimensional $p$-wave superconductor. We probe the black hole by changing the size of the interval and by fixing $q$ or $T$. We show that the universal part is finite across the superconductor phase transition and has competitive behaviors different from the finite part of entanglement entropy. The behavior of the subregion complexity depends on the gravitational coupling constant divided by the gauge coupling constant. When this ratio is less than the critical value, the subregion complexity increases as temperature becomes low. This behavior is similar to the one of the holographic $1+1$ dimensional $s$-wave superconductor arXiv:1704.00557. When the ratio is larger than the critical value, the subregion complexity has a non-monotonic behavior as a function of $q$ or $T$. We also find a discontinuous jump of the subregion complexity as a function of the size of the interval. The subregion complexity has the maximum when it wraps the almost entire spatial circle. Due to competitive behaviors between normal and condensed phases, the universal term in the condensed phase becomes even smaller than that of the normal phase by probing the black hole horizon at a large interval. It implies that the formed condensate decreases the subregion complexity like the case of the entanglement entropy.

22 pages, 14 figures, added computation of the holographic renormalized entanglement entropy, the version accepted for publication in PTEP

References in corpus (16)

• Building an AdS/CFT superconductor
• Entanglement as a Probe of Confinement
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• A c-theorem for the entanglement entropy
• On Volumes of Subregions in Holography and Complexity
• Holographic Entanglement Entropy in Insulator/Superconductor Transition
• Chiral anomalies and AdS/CMT in two dimensions
• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• Subregion Action and Complexity
• One-dimensional holographic superconductor from AdS_3/CFT_2 correspondence
• Entanglement Entropy and Complexity for One-Dimensional Holographic Superconductors
• Holographic complexity of anisotropic black branes
• Geometric Entropy and Hagedorn/Deconfinement Transition
• Holographic Entanglement Entropy in 2D Holographic Superconductor via $Ad{S}_3/CF{T}_2$
• 1+1-dimensional p-wave superconductors from intersecting D-branes

Cited by in corpus (6)

• Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductor
• Holographic Subregion Complexity in General Vaidya Geometry
• 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 Entanglement Entropy and Complexity for D-Wave Superconductors
• Kibble-Zurek Scaling in a Holographic p-wave Superconductor