Quasi-Particles in Two-Dimensional Hubbard Model: Splitting of Spectral Weight

Abstract

It is shown that the energy $(\epsilon )$ and momentum $(k)$ dependences of the electron self-energy function $\Sigma (k,\epsilon +i0)\equiv {\Sigma }^R(k,\epsilon )$ are, $\mathrm{Im}{\Sigma }^R(k,\epsilon )=-a{\epsilon }^2|\epsilon -{\xi }_k{|}^{-\gamma (k)}$ where $a$ is some constant, ${\xi }_k=\epsilon (k)-\mu ,\epsilon (k)$ being the band energy, and the critical exponent $\gamma (k)$, which depends on the curvature of the Fermi surface at $k$, satisfies, $0\le \gamma (k)\le 1$. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $\epsilon ,{\xi }_k\to 0$ but for ${\xi }_k\ne 0$ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.

arXiv comment8 pages (LaTeX) 4 figures available upon request will be sent by air mail. KomabaCM-preprint-O3

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