"Unraveling Luttinger's Theorem: The Quantum Rules Bend"

Research into Luttinger's theorem, which connects a system's particle capacity with its response to low-energy excitations, has revealed its failure in specific cases of strongly correlated phases of matter, particularly in topological insulators, highlighting a fundamental connection between particle behavior and quantum matter classification. A recent study by Lucila Peralta Gavensky, Subir Sachdev, and Nathan Goldman has shown that the failure of Luttinger's theorem and the classification of insulating states of matter are connected, with the Ishikawa-Matsuyama invariant fully characterizing correlated insulators when Luttinger's theorem is satisfied, but requiring corrections when it is violated, shedding light on the emergence of exotic phenomena in strongly correlated quantum matter.