Journal
SCIENCE
Volume 358, Issue 6367, Pages 1155-1160Publisher
AMER ASSOC ADVANCEMENT SCIENCE
DOI: 10.1126/science.aam7127
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Funding
- Simons Foundation through the Simons Collaboration on the Many Electron Problem
- NSF [DMR-1505406, DMR-1409510, ACI-1053575]
- U.S. Department of Energy (DOE) [DE-SC0008627]
- Simons Investigators Award
- DOE [DE-SC0008624]
- DOE Office of Science [DE-AC02-05CH11231]
- Oak Ridge Leadership Computing Facility at Oak Ridge National Lab
- European Research Council under the European Union's Horizon research and innovation program [677061]
- Deutsche Forschringsgemeinschaft (DFG) [NO 314/5-1, FOR 1807]
- U.S. Department of Energy (DOE) [DE-SC0008627, DE-SC0008624] Funding Source: U.S. Department of Energy (DOE)
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1505406, 1409510] Funding Source: National Science Foundation
- European Research Council (ERC) [677061] Funding Source: European Research Council (ERC)
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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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