Nonperturbative Calculations for Spectroscopic Properties of Cuprate High-Temperature Superconductors

We review nonperturbative numerical calculations on dynamical properties of the two-dimensional Hubbard model and their relevance to various spectroscopic experiments on high-temperature superconducting cuprates. The unbiased nonperturbative theories have revealed the existence of a self-energy singularity in slightly doped Mott insulators, which is responsible for both the pseudogap formation and high-temperature superconductivity. The self-energy pole traces back to the Mott gap at zero doping, underscoring that Mott physics lies at the heart of both the pseudogap and high temperature superconductivity. This mechanism of the pseudogap relies neither on competing order nor preformed pair while that of the high superconducting transition temperature does not necessitate a bosonic glue to mediate Cooper pairing. Instead, both mechanisms are linked to the singular self-energy inherent to the Mott insulator. The presence of the self-energy pole accounts for various spectroscopic anomalies reported so far in experiments, deforming the spectral structure in a manner beyond a simple mass renormalization. The low-energy electron dynamics, as computed with the self-energy pole, suggest the existence of a hidden fermionic excitation coupling to quasiparticles.