Ergotropy and entanglement in critical spin chains

A subsystem of an entangled ground state (GS) 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 GS, 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 one-dimensional critical states.

Automated summary

This study shows that a subsystem of an entangled ground state is in a mixed state. Therefore, by isolating this subsystem from its surroundings, we can extract energy using unitary transformations, up to a maximal amount known as ergotropy. After the energy is extracted, the subsystem still contains some bound energy above its local ground state, providing valuable information about the entanglement structure. The study also suggests that the bound energy for half a free fermionic chain decays as the square of the entanglement entropy divided by the chain length and this relation may hold for all one-dimensional critical states.