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Much Ado about Zeros: The Luttinger Surface and Mottness

Tudor D. Stanescu·Philip W. Phillips·Ting-Pong Choy
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Abstract

We prove that the Mott insulating state is characterized by a divergence of the electron self energy at well-defined values of momenta in the first Brillouin zone. When particle-hole symmetry is present, the divergence obtains at the momenta of the Fermi surface for the corresponding non-interacting system. Such a divergence gives rise to a surface of zeros (the Luttinger surface) of the single-particle Green function and offers a single unifying principle of Mottness from which pseudogap phenomena, spectral weight transfer, and broad spectral features emerge in doped Mott insulators. We also show that only when particle-hole symmetry is present does the volume of the zero surface equal the particle density. We identify that the general breakdown of Luttinger's theorem in a Mott insulator arises from the breakdown of a perturbative expansion for the self energy in the single-particle Green function around the non-interacting limit. A modified version of Luttinger's theorem is derived for special cases.

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Tudor D. Stanescu, Philip W. Phillips, Ting-Pong Choy. 2007-02-14. Much Ado about Zeros: The Luttinger Surface and Mottness. https://doi.org/10.1103/physrevb.75.104503

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