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Science

Tweaking the Hubbard model

Jelena Stajic

Published Sep 26, 2019• 0 citations
Publisher

Abstract

Superconductivity 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][1] [1]: /lookup/doi/10.1126/science.aal5304

DOI
10.1126/science.365.6460.1414-l

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Superconductivity
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
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
Quantum Simulation One of the simplest models of interacting fermions on a two-dimensional (2D) lattice—the Hubbard model—becomes too tricky to simulate on classical computers as the density of empty lattice sites (holes) increases. Chiu et al. used a quantum microscope to take snapshots of thousands of realizations of the 2D Hubbard model in an optical lattice filled with fermionic lithium atoms at varying hole densities (see the Perspective by Schauss). The authors used pattern recognition algorithms to analyze the images, in which each lattice site was individually resolved. Comparing these patterns to the predictions of several theoretical models, they found the most consistency with the so-called geometric string model. Science , this issue p. [251][1]; see also p. [218][2] [1]: /lookup/doi/10.1126/science.aav3587 [2]: /lookup/doi/10.1126/science.aax6486
The Hubbard and related models serve as a fundamental starting point in understanding the novel experimental phenomena in correlated electron materials, such as superconductivity, Mott insulator, magnetism. Recent numerical simulations demonstrate that the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a key role for the superconductivity. However, the impacts of long-range intersite interactions in such a ${t}^{\ensuremath{'}}$-Hubbard model are less explored. Using the state-of-art density-matrix renormalization group method, we investigate the ${t}^{\ensuremath{'}}$-Hubbard model on a two-leg ladder with the intersite interactions extended to the fourth neighbors. The numerical results show that the quasi-long-range superconducting correlation remains stable under the repulsive intersite interactions and these long-range repulsive interactions only change the ground state quantitatively. In addition, inspired by recent experiments on one-dimensional cuprate chain ${\mathrm{Ba}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$, we find that the nearest-neighbor attractive interaction significantly enhances the superconducting correlation when it is comparable to the nearest-neighbor hopping ttt. Stronger attraction drives the system into an electron-hole phase separation. Finally, we discuss the effects of the on-site interaction on superconductivity.
Abstract The issue of whether d -wave superconductivity (SC) occurs in the square-lattice Hubbard model with U of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-neighbor hopping in the range −0.5t≤t′≤0.25t-0.5t\le t^{\prime} \le 0.25t−0.5t≤t′≤0.25t − 0.5 t ≤ t ′ ≤ 0.25 t with U = 8 t and 12 t and doped hole concentrations δ = 1/12 and 1/8. For t′≤0t^{\prime} \le 0t′≤0 t ′ ≤ 0 , the ground-state appears to be a charge-density wave (CDW) of one sort or another with SC correlations that are extremely short-ranged. In contrast, in some cases, the local magnetic order has a correlation length greater than half the cylinder width - suggestive that magnetic order might also arise in the 2D limit. For t′ > 0t^{\prime}\,>\,0t′>0 t ′ > 0 , our results depend more strongly on boundary conditions (periodic vs antiperiodic), making it still harder to correctly guess whether SC or CDW correlations dominate in the 2D limit. These results were obtained employing matrix-product states with bond dimensions large enough that energy differences as small as 10 −3 t per site can be resolved.