Quantum criticality and mixed-state entanglement in holographic superconductor--insulator transitions

TL;DR

This paper investigates quantum criticality in a holographic superconductor-insulator transition, highlighting the effectiveness of entanglement wedge cross-section as a diagnostic tool over holographic entanglement entropy.

Contribution

It demonstrates that entanglement wedge cross-section robustly detects quantum critical points in holographic models, unlike holographic entanglement entropy.

Findings

Approaching the QCP closes the energy gap and induces insulating features.

EWCS shows critical scaling near the QCP, serving as a reliable diagnostic.

HEE is less sensitive to the transition due to dominance by thermal entropy.

Abstract

We study quantum criticality in a holographic Einstein--Maxwell--Dilaton--Axion (EMDA) p-wave superconductor exhibiting a superconductor--insulator transition (SIT). By tracking the superconducting energy gap, we show that approaching the quantum critical point (QCP) closes the gap and induces incipient insulating features, indicating that enhanced quantum fluctuations suppress superconducting order and trigger the SIT. We suggest that this behavior occurs only when the condensate orientation is aligned with the direction of translational symmetry breaking. To probe the transition, we employ two holographic indicators: holographic entanglement entropy (HEE) and the entanglement wedge cross-section (EWCS), the latter being a mixed-state entanglement measure. In contrast to HEE, which for sufficiently large configuration is dominated by the thermal entropy and is therefore largely insensitive to entanglement along the temperature direction, EWCS displays pronounced critical scaling and provides a robust diagnostic of the quantum phase transition (QPT). We attribute this contrast to the fact that HEE at large scales is controlled by the infrared (IR) geometry, whereas EWCS is governed by deformations of the entire bulk. Our results establish EWCS as a robust probe of holographic quantum criticality in mixed states.