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

Zheng, Bo-Xiao and Chung, Chia-Min and Corboz, Philippe and Ehlers, Georg and Qin, Ming-Pu and Noack, Reinhard M. and Shi, Hao and White, Steven R. and Zhang, Shiwei and Chan, Garnet Kin-Lic (2017) Stripe order in the underdoped region of the two-dimensional Hubbard model. Science, 358 (6367). pp. 1155-1160. ISSN 0036-8075.

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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.

Item Type:Article
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URLURL TypeDescription Paper Materials
White, Steven R.0000-0002-0831-9097
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2017 American Association for the Advancement of Science. Received 5 January 2017; accepted 17 October 2017. Work performed by B.-X.Z., C.-M.C., M.-P.Q., H.S., S.R.W., S.Z., and G.K.-L.C. was supported by the Simons Foundation through the Simons Collaboration on the Many Electron Problem. S.R.W. acknowledges support from the NSF (DMR-1505406), as do S.Z. and H.S. (DMR-1409510). M.-P.Q. was also supported by the U.S. Department of Energy (DOE) (DE-SC0008627). G.K.-L.C. acknowledges support from a Simons Investigators Award and the DOE (DE-SC0008624). DMET calculations were carried out at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by DE-AC02-05CH11231. AFQMC calculations were carried out at the Extreme Science and Engineering Discovery Environment, supported by the NSF (ACI-1053575); at the Oak Ridge Leadership Computing Facility at Oak Ridge National Lab; and at the computational facilities at the College of William and Mary. P.C. was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant no. 677061). G.E. and R.M.N. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) through grant no. NO 314/5-1 in Research Unit FOR 1807. Data used in this work are in the supplementary materials and online at The DMET calculations were performed with the DMET library, available online at The real-space DMRG calculations were performed with ITensor, available online at Access to the other computer codes can be arranged with the authors upon reasonable request: For the AFQMC code, please contact S.Z.; for the hybrid DMRG code, please contact R.M.N.; and for the iPEPS code, please contact P.C.
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0008627
Department of Energy (DOE)DE-SC0008624
Department of Energy (DOE)DE-AC02-05CH11231
College of William and MaryUNSPECIFIED
European Research Council (ERC)677061
Deutsche Forschungsgemeinschaft (DFG)314/5-1
Issue or Number:6367
Record Number:CaltechAUTHORS:20170127-174736374
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Official Citation:Stripe order in the underdoped region of the two-dimensional Hubbard model BY BO-XIAO ZHENG, CHIA-MIN CHUNG, PHILIPPE CORBOZ, GEORG EHLERS, MING-PU QIN, REINHARD M. NOACK, HAO SHI, STEVEN R. WHITE, SHIWEI ZHANG, GARNET KIN-LIC CHAN SCIENCE01 DEC 2017 : 1155-1160
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73807
Deposited By: Donna Wrublewski
Deposited On:28 Jan 2017 19:48
Last Modified:09 Mar 2020 13:19

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