Research Article

Stripe order in the underdoped region of the two-dimensional Hubbard model

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Science  01 Dec 2017:
Vol. 358, Issue 6367, pp. 1155-1160
DOI: 10.1126/science.aam7127

Numerics converging on stripes

The Hubbard model (HM) describes the behavior of interacting particles on a lattice where the particles can hop from one lattice site to the next. Although it appears simple, solving the HM when the interactions are repulsive, the particles are fermions, and the temperature is low—all of which applies in the case of correlated electron systems—is computationally challenging. Two groups have tackled this important problem. Huang et al. studied a three-band version of the HM at finite temperature, whereas Zheng et al. used five complementary numerical methods that kept each other in check to discern the ground state of the HM. Both groups found evidence for stripes, or one-dimensional charge and/or spin density modulations.

Science, this issue p. 1161, p. 1155


Competing inhomogeneous orders are a central feature of correlated electron materials, including the high-temperature superconductors. The two-dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models, even in challenging settings.

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