• quantum phase transitions
• quantum thermodynamics
• dmrg
• quantum correlations
• spin chains

In this work, we study two quantum thermodynamic quantities near the quantum critical points of the XY and XXZ model at zero temperature. The first one, ergotropy, is the solution to the work extraction problem in a quantum setting. The second one is a new quantity, we called it "max-ergotropy", that quantifies the maximum energy difference achievable acting by unitary operations on a quantum state. Both ergotropy and max-ergotropy proved to be excellent quantum phase transition markers for the XY and the XXZ models. Furthermore, the study of these quantities reveals some new insights on the interplay between energy and correlations in a quantum system.