Characterization of Quantum Phase Transition using Holographic Entanglement Entropy

TL;DR

This paper explores how holographic entanglement entropy can characterize quantum phase transitions, especially near critical points, using a novel holographic model with metal-insulator transitions that exhibit extremal behavior in entropy derivatives.

Contribution

It demonstrates that the derivative of holographic entanglement entropy exhibits extremal behavior near quantum critical points, proposing a universal feature for characterizing quantum phase transitions holographically.

Findings

Holographic entanglement entropy derivative shows extremal behavior near QCPs

Constructed backgrounds exhibit metal-insulator transitions with zero entropy density at zero temperature

Proposed HEE derivatives as universal indicators of quantum phase transitions

Abstract

The entanglement exhibits extremal or singular behavior near quantum critical points (QCPs) in many condensed matter models. These intriguing phenomena, however, still call for a widely accepted understanding. In this letter we study this issue in holographic framework. We investigate the connection between the holographic entanglement entropy (HEE) and the quantum phase transition (QPT) in a lattice-deformed Einstein-Maxwell-Dilaton theory. Novel backgrounds exhibiting metal-insulator transitions (MIT) have been constructed in which both metallic phase and insulating phase have vanishing entropy density in zero temperature limit. We find that the first order derivative of HEE with respect to lattice parameters exhibits extremal behavior near QCPs. We propose that it would be a universal feature that HEE or its derivatives with respect to system parameters can characterize QPT in a generic holographic system. Our work opens a window for understanding the relation between entanglement and the QPT from holographic perspective.