Quickly confirmed in systems with independent particles, this theorem remains applicable in correlated quantum systems identified by intense inter-particle interactions.However, and quite remarkably, Luttingers theorem has actually been revealed to stop working in extremely particular and exotic instances of strongly associated stages of matter. Really just recently, nevertheless, theorists identified exotic designs of associated insulators that mysteriously elude this enticing category: corrections to the Ishikawa-Matsuyama invariant are therefore needed in strange settings.Connection Between Luttingers Theorem and Insulating State ClassificationWriting in the distinguished Physical Review Letters, Lucila Peralta Gavensky and Nathan Goldman (ULB), together with Subir Sachdev (Harvard), reveal that the failure of Luttingers theorem and the classification of insulating states of matter are connected by an essential relation. In essence, these authors show that the Ishikawa-Matsuyama invariant completely characterizes correlated insulators whenever Luttingers theorem is satisfied.In contrast, this topological invariant is shown to be insufficient to label correlated stages as soon as Luttingers theorem is breached, and the authors offer explicit expressions for the required corrections in terms of pertinent physical quantities.This essential connection in between Luttingers theorem and the topological classification of quantum matter sheds light on the introduction of unique phenomena in strongly associated quantum matter.Reference: “Connecting the Many-Body Chern Number to Luttingers Theorem through Středas Formula” by Lucila Peralta Gavensky, Subir Sachdev and Nathan Goldman, 4 December 2023, Physical Review Letters.DOI: 10.1103/ PhysRevLett.131.236601.
