Illinois physicists extend quantum phase stability rules to systems that leak into their environment

"The most important idea in defining a phase of matter is that it should be stable. It should be defined in such a way that if you perturb the state slightly, it still stays in the same phase," Jong Yeon Lee, an Illinois physics professor, said ^[6]. For an isolated system that test has an exact form. "For pure states, this notion is well defined: two states belong to the same phase if their local parent Hamiltonians can be connected without closing the energy gap, while an unavoidable gap closing signals a phase transition," Lee said ^[7].

Physicists use pure states to describe closed quantum systems because they are tractable, and classifying their phases rests on the structure of gapped Hamiltonians ^[5]. Pure states are also an idealization. A real system interacts with its surroundings and decoheres into a mixed state, which phys.org's account calls an unpredictable statistical mess ^[8]. Classifying phases in these open, nonequilibrium systems has posed numerous technical challenges, according to the same report ^[2].

Topological phases are why the question matters. Lev Landau's symmetry-based scheme from the 1930s covers solids, liquids, gases, magnets and superconductors ^[3]. Since the 1980s, though, physicists have known that many phases also need topology to describe ^[4]. Topological phases are labeled by invariants that do not change under continuous deformation, and they keep their order when perturbed locally ^[4][11]. They store information spread across the whole system. According to phys.org, that resilience makes them candidates for quantum-computing hardware, which is notoriously vulnerable to environmental noise ^[11].

The Illinois framework comes from the Anthony J. Leggett Institute for Condensed Matter Theory and generalizes the closed-system principles to the open case ^[1]. According to phys.org, it overcomes shortcomings of current classification schemes and distinguishes a wider range of quantum phenomena than before ^[10]. The report's headline is more specific: the new stability rules separate phases that an older method wrongly groups together ^[9]. The report did not identify the older method, the phases it merged, or what replaces the energy-gap condition once a state is mixed.

Whether the distinction can be seen in a laboratory is an open question. The work is a theoretical classification framework ^[1]. In our view the work matters in practice only if two mixed states that the older scheme filed together differ in something a device cares about, such as whether stored information survives. If they do, we'd expect the new rules to change which noisy states count as protected, because resistance to local perturbations is the property hardware designers want from topological phases ^[11].