Absence of superconductivity in the pure two-dimensional Hubbard model

TL;DR

This study investigates the ground state of the doped two-dimensional Hubbard model using advanced computational methods, finding no evidence of superconductivity in the parameter regime relevant to cuprate high-temperature superconductors.

Contribution

The paper provides a comprehensive comparison of AFQMC and DMRG methods, demonstrating the absence of superconductivity in the pure 2D Hubbard model at intermediate to strong coupling.

Findings

No superconducting correlations found near optimal doping

Validation of AFQMC with DMRG on small systems

Establishment of non-superconducting ground state in the studied regime

Abstract

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 non-superconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.