Research Article

Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t

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Science  27 Sep 2019:
Vol. 365, Issue 6460, pp. 1424-1428
DOI: 10.1126/science.aal5304

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Tweaking the Hubbard model

Modeling high-temperature superconductivity (HTS) remains extremely challenging. Many researchers believe that the simplest model that captures HTS is the Hubbard model, which accounts for interactions and allows for electrons to hop from one site of a lattice to another. However, even just determining whether the ground state of this model supports superconductivity is tricky. Jiang and Devereaux undertook an extensive computational study based on a method known as density matrix renormalization group. They found that for a particular concentration of empty lattice sites, superconductivity indeed appears as a long-range state, but only if electrons are allowed to hop to sites that are next to their immediate neighbors on the lattice.

Science, this issue p. 1424


The Hubbard model is widely believed to contain the essential ingredients of high-temperature superconductivity. However, proving definitively that the model supports superconductivity is challenging. Here, we report a large-scale density matrix renormalization group study of the lightly doped Hubbard model on four-leg cylinders at hole doping concentration δ = 12.5%. We reveal a delicate interplay between superconductivity and charge density wave and spin density wave orders tunable via next-nearest neighbor hopping t′. For finite t′, the ground state is consistent with a Luther-Emery liquid with power-law superconducting and charge density wave correlations associated with half-filled charge stripes. In contrast, for t′ = 0, superconducting correlations fall off exponentially, whereas charge density and spin density modulations are dominant. Our results indicate that a route to robust long-range superconductivity involves destabilizing insulating charge stripes in the doped Hubbard model.

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