spin liquid

superconductivity

cuprate superconductors

superconducting state

superconductors

anderson model

order parameter

hubbard model

superconducting transition

Physical Review X

We study the superconducting pairing correlations in the ground state of the doped Hubbard model—in its original form without hopping beyond nearest neighbor or other perturbing parameters—in two dimensions at intermediate to strong coupling and near optimal doping. The nature of such correlations has been a central question ever since the discovery of cuprate high-temperature superconductors. Despite unprecedented effort and tremendous progress in understanding the properties of this fundamental model, a definitive answer to whether the ground state is superconducting in the parameter regime most relevant to cuprates has proved exceedingly difficult to establish. In this work, we employ two complementary, state-of-the-art, many-body computational methods—constrained-path (CP) auxiliary-field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG) methods—deploying the most recent algorithmic advances in each. Systematic and detailed comparisons between the two methods are performed. The DMRG is extremely reliable on small width cylinders, where we use it to validate the AFQMC. The AFQMC is then used to study wide systems as well as fully periodic systems, to establish that we have reached the thermodynamic limit. The ground state is found to be nonsuperconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.14 MoreReceived 6 November 2019Revised 27 April 2020Accepted 19 May 2020DOI:https://doi.org/10.1103/PhysRevX.10.031016Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasSuperconductivityPhysical SystemsStrongly correlated systemsTechniquesDensity matrix renormalization groupHubbard modelQuantum Monte CarloCondensed Matter, Materials & Applied Physics

Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model