Tensor network simulations of electron-phonon coupling in the three band Hubbard model

It is believed that the CuO₂ plane captures the essential features of high-T_c cuprates. To date, most numerical and analytical efforts towards understanding superconductivity in these materials has been via the effective one-band Hubbard model, which eliminates the oxygen degrees of freedom via the Zhang-Rice construction. This comes at the cost of modelling the undoped system as a Mott insulator instead of a charge-transfer insulator, thereby missing potentially important physics such as the role of oxygen p-bands as non-trivial hole carriers. Here we build upon prior Density-Matrix Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) studies of the two-leg Three Band Hubbard (TBH) model by performing tensor network simulations of the TBH model with electron-phonon coupling. Various susceptibilities are measured towards the aim of clarifying the specific role of the copper d_x²-y² and oxygen p_x,y orbital degrees of freedom in mediating high-T_c superconductivity. Connections to the phase diagram of the cuprates are discussed.