Is there stripe order or d-wave superconductivity in the Hubbard model?*

In a recent paper Bo-Xiao Zheng et al. (arXIV:1701.00054) have claimed that, by using several state of the art numerical techniques, at a particular filling δ =1/ 8 and strong coupling U/t=8, the ground state of the Hubbard model displays charge and spin modulations that are typical of the so called stripe order. In this work we reconsider this model by using standard variational techniques based on quantum Monte Carlo[1]. We use a wider class of variational wavefunctions with a very accurate and systematically convergent description of the ground state properties[2,3]. The final aim of this work is to solve the apparent controversy between standard variational techniques based on Jastrow correlated mean-field approximations, apparently favoring the uniform d-wave superconducting solution and DMRG, tensor-network approximations, on the other hand biased for low entanglement entropy ground states.

[1] F. Becca and S. Sorella '' Quantum Monte Carlo Approaches for Correlated Systems ", Cambridge University Press (2017).
[2] L.F. Tocchio, F. Becca, A. Parola, and S. Sorella, Phys. Rev. B 78, 041101 (2008); Luca F. Tocchio, Federico Becca, and Sandro Sorella Phys. Rev. B 94, 195126 (2016).
[3] S. Sorella Phys. Rev.B 84, 241110 (2011).