Ergotropy and entanglement in critical spin chains

TL;DR

This paper investigates the relationship between ergotropy, entanglement, and bound energy in critical spin chains, revealing how bound energy diminishes with system size and entanglement, providing insights into quantum thermodynamics and entanglement structure.

Contribution

It establishes a quantitative relation between bound energy and entanglement entropy in critical spin chains, proposing a universal decay behavior for 1D critical states.

Findings

Bound energy decays as the square of entanglement entropy divided by chain length

For large systems, the bound energy approaches zero

Conjecture that the relation holds for all 1D critical states

Abstract

A subsystem of an entangled ground state is in a mixed state. Thus, if we isolate this subsystem from its surroundings we may be able to extract work applying unitary transformations, up to a maximal amount which is called ergotropy. Once this work has been extracted, the subsystem will still contain some bound energy above its local ground state, which can provide valuable information about the entanglement structure. We show that the bound energy for half a free fermionic chain decays as the square of the entanglement entropy divided by the chain length, thus approaching zero for large system sizes, and we conjecture that this relation holds for all 1D critical states.