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arXiv · 1906.12071

Dynamical $t/U$ Expansion of the Doped Hubbard Model

Wenxin Ding·Rong Yu
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Abstract

We construct a new $U(1)$ slave spin representation for the single band Hubbard model in the large-$U$ limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green's function theory for slave spins, we calculate the single-particle spectral function of electrons, and the result is comparable to that in dynamical mean field theories. We then formulate a dynamical $t/U$ expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a $t-J$ model for spinons self-consistently coupled to n $XXZ$ model for the slave spins. We show that the superexchange $J$ is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite $U$ limit, as a manifestation of the Nagaoka ferromagnetism.

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Wenxin Ding, Rong Yu. 2019-06-28. Dynamical $t/U$ Expansion of the Doped Hubbard Model. https://doi.org/10.1088/0256-307x%2F41%2F3%2F037101

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