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Physicists at the University of Illinois have developed a new framework to classify nonequilibrium quantum phases of matter, addressing limitations in older methods that group distinct phenomena together. While traditional classification relies on symmetry and topology for isolated systems, categorizing open systems that interact with their environment has been difficult due to technical challenges hindering understanding of new quantum behaviors.

The researchers, led by professor Jong Yeon Lee, propose a method called entanglement bootstrapping. This approach identifies stability criteria by finding fixed points where system parameters remain consistent across different length scales. Unlike pure states in closed systems described by Hamiltonians, real-world mixed states degrade through interaction with their environment and lack these traditional mathematical descriptions.

To define stable phases for mixed states, the team established three specific conditions. The first condition ensures that physically separated regions do not significantly affect each other, preventing long-range correlations from destabilizing the system. The second condition requires that if information in a local region is lost, its surrounding neighborhood can recover it, reflecting how topological information is stored nonlocally across the entire system. A third mathematical condition ensures the states remain tractable for analysis.