Information geometry of quantum critical submanifolds: Relevant, marginal, and irrelevant operators

We analyze the thermodynamical limit of quantum metric along critical submanifolds theory space. Building upon various results previously known in literature, we relate its singular behavior to normal directions, which are naturally associated with relevant operators renormalization group sense. formulate these language information and differential geometry. exemplify our through paradigmatic examples XY Haldane models, where directions seen be precisely those has behavior, while for tangent ones it vanishes -- lie kernel metric.