Criticality and entanglement in random quantum systems

TL;DR

This paper reviews how entanglement entropy behaves in strongly disordered quantum systems at critical points, revealing universal features and differences from pure systems, with implications for understanding quantum criticality and localization.

Contribution

It provides a comprehensive review of universal entanglement properties at random quantum critical points, highlighting differences from pure systems and discussing measurement techniques and higher-dimensional challenges.

Findings

Entanglement entropy shows universal logarithmic divergence at critical points.

Disorder-averaged entanglement entropy reveals insights into quantum criticality.

Universal coefficients differ from those in pure systems, indicating unique critical behavior.

Abstract

We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random ("pure") quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.