Competition among superconducting, antiferromagnetic, and charge orders with intervention by phase separation in the 2D Holstein-Hubbard model

Although the electron-phonon interactions play important roles in various phenomena of condensed matter, their roles are less understood in strongly-correlated electrons such as high-T_c cuprates. For studies on strongly-correlated electrons, there are several numerical methods. Among them, the variational Monte Carlo (VMC) method takes the advantage of wide applicability without the notorious sign problem. Recently, we have extended this method to electron-phonon coupled systems.
In this work, using the VMC method, we study the ground state of Holstein-Hubbard model on a square lattice [2]. At half filling, an extended intermediate metallic or weakly superconducting (SC) phase emerges, sandwiched by antiferromagnetic and charge order (CO) insulating phases. By the carrier doping into the CO insulator, the SC order dramatically increases for strong electron-phonon couplings, but largely hampered by wide phase separation (PS) regions. Superconductivity is optimized at the border to the PS. [1] T. Ohgoe and M. Imada, arXiv: 1703.08899 (accepted in Phys. Rev. Lett.)