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

TL;DR

This paper investigates the holographic subregion complexity of a 1+1 dimensional p-wave superconductor using a 3D black hole with vector hair, revealing phase transition behaviors and the influence of gravitational and gauge couplings.

Contribution

It introduces the analysis of subregion complexity in a holographic p-wave superconductor and explores its dependence on temperature, charge, and coupling constants, highlighting novel phase transition features.

Findings

Universal part of complexity remains finite across phase transition.

Complexity behavior depends on the ratio of gravitational to gauge coupling.

Discontinuous jump in complexity occurs with interval size.

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.