| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Dynamical $t/U$ Expansion of the Doped Hubbard Model |
| Wenxin Ding1,2* and Rong Yu3 |
1School of Physics and Material Science, Anhui University, Hefei 230601, China
2Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
3Physics Department and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University, Beijing 100872, China
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| Cite this article: |
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Wenxin Ding and Rong Yu 2024 Chin. Phys. Lett. 41 037101 |
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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. 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 an $XXZ$ 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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Received: 22 November 2023
Published: 19 March 2024
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| PACS: |
71.10.Fd
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(Lattice fermion models (Hubbard model, etc.))
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11.15.Me
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(Strong-coupling expansions)
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