A short review on entanglement in quantum spin systems

TL;DR

This paper reviews recent advances in understanding entanglement entropy in quantum spin systems, focusing on scaling laws, area law, and implications for quantum phase transitions and computation.

Contribution

It provides a comprehensive overview of entanglement properties in many-body quantum systems, highlighting recent progress and key concepts like area law and entanglement dynamics.

Findings

Entanglement entropy scales with system size at quantum critical points.

Area law governs entanglement in ground states of local Hamiltonians.

Entanglement dynamics influence quantum computation and phase transitions.

Abstract

We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.