Quantum correlation and phase transition

Just look at boiling water to see the spectacular changes in the organization of matter during a phase change. At the quantum level, phase transitions also involve significant changes, especially in a very quantum phenomenon, entanglement.

In a recent article in Physical Review Letters, a team of theorists from Institut quantique (Pr David Poulin and Pr André-Marie Tremblay), Royal Holloway in London (Caitlin Walsh, student and Pr Giovanni Sordi) and Brookhaven Laboratory in the United States (Patrick Sémon, research scientist) have combined concepts of quantum information and quantum materials to highlight quantum correlations during a phase transition that is fundamental for quantum materials.

The research initiated by Giovanni Sordi focused on a mathematical model where interactions between electrons transform a metal, where electrons can move freely, into an insulator, where electrons are localized. This transition between metal and insulator, also known as the Mott transition, is a central phenomenon for the theory of quantum materials, such as high temperature superconductors.

Similar to the liquid-gas transition that is familiar to us with boiling water, this metal-insulator transition has two key characteristics: it is abrupt at low temperature and ends at high temperature at a critical point where there is no longer any difference between the two phases. The important discovery of this team was to show that all these characteristics are manifested in key measurements of quantum correlations. In particular, they identified how electrons were entangled and how mutual information changes at the transition. Electrons are entangled when the measurement of the state of an electron instantly changes the state of other electrons. And mutual information informs us of the presence of correlations, whatever their nature. These two quantities are related to generalizations of the entropy concept.

The results of this theory can be verified by advanced experiments using quantum simulators made of ultra cold atoms where it is possible to measure quantum correlations.