# Entanglement Entropy and Complexity for One-Dimensional Holographic Superconductors

## TL;DR

This paper investigates the behavior of holographic complexity in one-dimensional superconductors, revealing it differs from entanglement entropy but still signals phase transitions at the same critical temperature.

## Contribution

It provides a numerical analysis clarifying the differing behaviors of holographic complexity and entanglement entropy during phase transitions in 1D holographic superconductors.

## Key findings

- Holographic complexity does not mirror entanglement entropy during phase transitions.
- Universal terms of both quantities are finite and indicate the critical temperature.
- Complexity and entanglement entropy reflect phase transitions differently.

## Abstract

Holographic superconductor is an important arena for holography, as it allows concrete calculations to further understand the dictionary between bulk physics and boundary physics. An important quantity of recent interest is the holographic complexity. Conflicting claims had been made in the literature concerning the behavior of holographic complexity during phase transition. We clarify this issue by performing a numerical study on one-dimensional holographic superconductor. Our investigation shows that holographic complexity does not behave in the same way as holographic entanglement entropy. Nevertheless, the universal terms of both quantities are finite and reflect the phase transition at the same critical temperature.