Do the single band Hubbard models describe superconductivity in the cuprates?*

Since the beginnings of high temperature superconductivity in the cuprates, a key theoretical question has been whether the single band Hubbard model and its cousin, the t-J model, describe the superconductivity at least qualitatively.  While initially this seemed like a simple question, the physics of both the cuprates and the models is now known to be much more complicated.  A key complication is the presence of spontaneously formed striped arrangements of holes, which have been argued (by different people!) to either enhance or to suppress superconductivity.  The models are very challenging to simulate, but even harder to treat analytically.  

In this talk I will try to answer this question in two different ways. The first version of the question is: does the single band t-t' Hubbard model have d-wave superconducting ground states, on both the hole and electron doped sides, with stronger pairing for hole doping? Our recent results using a combination of the density matrix renormalization group and constrained path quantum Monte Carlo, extrapolated to the 2D thermodynamic limit, indicate that the answer is yes[arXiv:2303.08376]. Here, the answers for the Hubbard model are different from those of the t-J model, which exhibits much stronger pairing on the electron doped side.

The second version of the question is: when considered from a downfolding framework, does the single band t-t' Hubbard model have all the important interaction terms which should be included to capture superconductivity even qualitatively?  Here, I will argue that the answer is no: an important density-assisted hopping term which is not part of the standard Hubbard model has a very large coefficient and has a significant effect on pairing. This is based on a downfolding of the three-band Hubbard model using Wannier functions constructed using DMRG ground states[arXiv:2303.00756].  Unlike many downfolding methods, this approach generates all possible interaction terms, which can be truncated based on the magnitude of their coefficients. 

While the contrasting answers to these two versions of the same question indicate a subtle and complicated theoretical landscape, they also show that simulations are approaching the point where they give reliable quantitative predictions for the cuprates.