In 1960, Luttinger proposed a universal principle connecting the total capacity of a system for particles with its response to low-energy excitations. Although easily confirmed in systems with independent particles, this theorem remains applicable in correlated quantum systems characterized by intense inter-particle interactions.
However, and quite surprisingly, Luttinger’s theorem has been shown to fail in very specific and exotic instances of strongly correlated phases of matter. The failure of Luttinger’s theorem and its consequences on the behavior of quantum matter are at the core of intense research in condensed matter physics.
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