Bound states in doped charge transfer insulators

Understanding the physics of doping a charge transfer insulator is the most important problem in high-temperature superconductivity. In this work, we show that an in-gap bound state emerges from the localized hole of the doped charge transfer insulator. We propose an approximate ground state wavefunction based on one localized Zhang-Rice singlet and the Neel state. By calculating the excitation states with one hole added and removed from this ground state, we successfully identify the existence of bound states inside the charge transfer gap. This feature is further proved by the MPS-based Lanczos study of a system of $4\times4$ CuO$_2$ unit cells. How these bound states evolve into metallic states is further discussed. Our findings identify the key component of recent STM results on lightly doped Ca$_2$CuO$_2$Cl$_2$ and provide a new understanding of hole-doped charge transfer insulators.