Gobal entanglement and double occupancy in many-electron states

TL;DR

This paper explores how different many-electron states, including metallic, strongly-correlated, and superconducting states, exhibit varying levels of quantum entanglement, influenced by factors like double occupancy and energy gap.

Contribution

It provides explicit calculations of entanglement in Gutzwiller-projected states and analyzes how double occupancy affects entanglement in various electron states.

Findings

Uncorrelated metallic states at half filling maximize entanglement.

Gutzwiller projection reduces entanglement by inhibiting double occupancy.

Superconducting states show lower entanglement than metallic states, with possible nonzero single-site concurrence.

Abstract

The entanglement in many-electron states is investigated using a global entanglement measure, viz. average site mixedness. We have examined metallic states of noninteracting electrons, Nagaoka and Gutzwiller states of strongly-correlated electrons, and superconducting states. Uncorrelated metallic states at half filling seem to maximize entanglement, as these states optimize the number of holes, the number of doubly-occupied sites. Entanglement is calculated explicitly for Gutzwiller-projected many-electron states in one dimension, which have less entanglement as double occupancy is inhibited in these states. Entanglement in superconducting states, which tend to promote double occupancy, is calculated as a function of the energy gap, and found to be lower than the metallic state entanglement. There is a possibility of a regime with a nonzero single-site concurrence depending on the energy gap.