We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states where $d$-wave superconductivity coexists with spatially nonuniform magnetic and charge order and find that they are energetically favored in a large doping region as compared to the uniform solution. We also study the spatial form of the density and the superconducting and magnetic order parameters at different doping values.

• Received 3 September 2017
• Revised 22 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.075112