Scaling of the entanglement spectrum near quantum phase transitions

TL;DR

This paper investigates how the entanglement spectrum scales near quantum phase transitions, providing analytical and numerical insights into its role in identifying critical points and phase characteristics.

Contribution

It derives the scaling properties of the entanglement spectrum near quantum phase transitions, including both integrable and non-integrable models, and demonstrates its effectiveness in locating critical points.

Findings

Scaling of the entanglement spectrum accurately indicates critical points.

Difference between the two largest Schmidt eigenvalues reveals mass scaling exponents.

Analytical and numerical methods confirm the universality of the scaling behavior.

Abstract

The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling properties in the vicinity of some integrable quantum phase transitions and extend our studies also to non integrable quantum phase transitions in one dimensional spin models numerically. Our analysis shows that, in all studied cases, the scaling of the difference between the two largest non degenerate Schmidt eigenvalues yields with good accuracy critical points and mass scaling exponents.