Abstract
The strong mutual repulsion of electrons is responsible for some of the most interesting phenomena in contemporary condensed matter physics, where examples range from unconventional high-temperature superconductivity, over quantum criticality to Mott metal-to-insulator transitions. Despite the intense research on the quantum many-body problem over the last decades, many of its aspects have not yet been fully understood. Recent progress, however, has been achieved by the application of so-called multi-method, multi-messenger studies of the most fundamental model for electronic correlations, the Hubbard model [1,2].
In the first part of the talk, I will present such a study of the half-filled two-dimensional Hubbard model on a simple square lattice at small values of the local Coulomb interaction [1]. I will demonstrate that the footprints of spin fluctuations can be tracked by a rich series of crossovers in multiple observables by multiple numerical techniques. In the second part of the talk, I will show how one can determine which fluctuation channel (charge, spin, particle-particle) is responsible for spectral properties such as the pseudogap in the strong coupling regime, directly relevant to cuprates. For this I will introduce the so-called "fluctuation diagnostics" approach [3,4], which can be utilized on top of diverse numerical methods, making it a helpful tool for future multi-method studies of strongly correlated phenomena.
