Persistent entanglement in a class of eigenstates of quantum Heisenberg spin glasses

TL;DR

This paper investigates eigenstates of a quantum Heisenberg spin glass, revealing a class of states with anomalously high delocalization and entanglement, and explores how different quantum states exhibit distinct entanglement scaling despite similar localization.

Contribution

It identifies and characterizes a novel class of eigenstates with enhanced delocalization and entanglement, and introduces random promoted two-particle states to explain their properties.

Findings

Anomalous eigenstates are more delocalized and entangled.

Random promoted two-particle states scale like generic random states.

Entanglement scaling differs from localization measures across state classes.

Abstract

The eigenstates of a quantum spin glass Hamiltonian with long-range interaction are examined from the point of view of localisation and entanglement. In particular, low particle sectors are examined and an anomalous family of eigenstates is found that is more delocalised but also has larger inter-spin entanglement. These are then identified as particle-added eigenstates from the one-particle sector. This motivates the introduction and the study of random promoted two-particle states, and it is shown that they may have large delocalisation such as generic ran- dom states and scale exactly like them. However, the entanglement as measured by two-spin concurrence displays different scaling with the total number of spins. This shows how for different classes of complex quantum states entanglement can be qualitatively different even if localisation measures such as participation ratio are not.