My research journey started in 2009 during my undergraduate studies. At the time, I was still living in the classical world: I had no idea about how the mathematical formalism of quantum mechanics worked, nor have been exposed to any course with a glance on what second quantization could be used for. Luckily, nice masters with artistic skills exist to teach us what a $c_j^\dagger$ means with lines and circles. Thanks to my advisor, there I was, starting my first project on the transport properties of single electron transistors, and learning about the Kondo problem. It opened my eyes to admire the beauty of many-body phenomena.

From my first NRG and ED codes to the daily routine of implementing td-DMRG calculations as a postdoc, I was falling in love for strongly correlated systems, and fascinated by numerical methods to (possibly) solve them.

Over the past years, I have been flirting with a few topics within this realm. I discuss them below.

Kondo effect in quantum dots

Interest in anomalous transport in correlated materials dates back to the 30s, increasing substantially with the proposal of the celebrated Kondo model and Numerical Renormalization-Group (RG) three decades later. The fabrication of the first single electron transistor to control the Kondo effect opened the way to explore anomalous transport to design novel quantum technologies. A realistic description of correlated transport, however, is a challenging theoretical problem. It depends, from one side, on precise band structure calculations and, on the other, on an accurate modeling of transport accounting for particle interactions. The lack of a single tool suiting both requirements, inspired a plethora of hybrid methods, as for instance, ab-initio and dynamical mean-field theory. By carrying out an RG analysis of the Anderson model we demonstrated that, under conditions of experimental interest, the high and low temperature fixed points are connected by an universal RG flow. At high temperatures, the weak-coupling fixed point is within the reach of local-density approximations. By contrast, as the temperature decreases, entanglement builds up, so that non-local correlations have to be taken for an RG method. We then proposed a self-consistent method in which Density Functional Theory (DFT) is employed to treat the weak-coupling system and the Numerical Renormalization-Group flow is used to correct the conductance in the strong coupling regime at low temperature. The method has been illustrated in a single-electron transistor close to zero bias. I am aware of a variety of novel implementations recently proposed with the capacity to treat more complex nanostructures, including out-of-equilibrium.

Time and momentum resolved spectroscopies

Experimental advances in spectroscopies have allowed probing excitations of quantum materials with unprecedented resolution. Facilities worldwide have capabilities to operate state-of-the-art techniques, such as angle-resolved photoemission (ARPES), inelastic neutron scattering (INS), and X-ray absorption (XAS) Resonant Inelastic X-ray scattering (RIXS). The fascinating data being collected in novel materials has motivated the interest of theorists to understand the excitation mechanisms responsible for the spectral features observed in the experiments. For strongly correlated matter this is, however, a very challenging task. Even at the level of model Hamiltonians and perturbation theory, calculating response functions is difficult because it involves a huge set of eigenstates. Aiming to overcome the limitations of the available analytical and numerical tools, we proposed a new framework inspired by the idea of quantum tunneling. It was originally illustrated to simulate the momentum-resolved spectrum probed by ARPES, and core-level spectroscopies and neutron scattering. One of the main advantages of our approach is that it provides the spectrum directly in the frequency domain, without the need to Fourier transform two-point correlation functions in time and filter the results to resolve low-lying excitations. While this approach has been applied to one-dimensional Mott insulators in and out-of-equilibrium and implemented by means of the time-dependent Density Matrix Renormalization-Group (td-DMRG), a future perspective is to extend it to more general models (including 2D) and use other numerical solvers. An interesting application that our approach that I intend to explore is inspired by a recent experimental paper proposing an alternative way to probe entanglement by connecting the spin excitation spectrum with the Quantum Fisher information.

Papers