Avalanche of entanglement and correlations at quantum phase transitions

TL;DR

This paper investigates how entanglement and correlations evolve in the quantum Ising and Bose-Hubbard models during phase transitions, revealing an entanglement cascade and hierarchy inversion that challenge mean-field approximations.

Contribution

It uncovers a sequential entanglement increase and hierarchy inversion at quantum phase transitions, highlighting a general phenomenon beyond specific models.

Findings

Entanglement depth increases with coupling strength in the Ising model.

Hierarchy inversion occurs where four-point correlations surpass lower-order correlations.

Similar behavior observed in the Bose-Hubbard model, indicating generality.

Abstract

We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling $J$ and find a sequential increase of entanglement depth with growing $J$. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for $J=\infty$, arriving at pure $\ell$-partite (GHZ type) entanglement of all $\ell$ spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small $J$. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should have far reaching consequences for approximations starting from a mean-field limit.