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, my love for numerical methods to simulate strongly correlated systems was growing bold.

Over the past years, I have been flirting with interesting 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, and increased 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 capable of controlling the Kondo effect opened the way to exploring anomalous transport in nanoscale devices. That was a time when quantum technologies as we know today were in their infancy.

A realistic description of correlated transport, however, remains a challenging theoretical problem. It depends, on the one hand, 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 the development of hybrid methods. For example, ab-initio and dynamical mean-field theory offer a nice framework to study transport in molecular transistors.

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 framework 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 was illustrated in a single-electron transistor close to zero bias. I am aware of more recent developments proposed and their capacity to treat more complex nanostructures, including out-of-equilibrium.

Time and momentum resolved spectroscopies

Experimental advances in spectroscopies have enabled the probing of excitations in quantum materials with unprecedented resolution. Facilities worldwide now operate state-of-the-art techniques such as angle-resolved photoemission (ARPES), inelastic neutron scattering (INS), X-ray absorption (XAS), and resonant inelastic X-ray scattering (RIXS). The fascinating data collected in novel materials has motivated theorists to understand the excitation mechanisms responsible for the spectral features observed in experiments. For strongly correlated matter, however, this remains a very challenging task. Even at the level of model Hamiltonians and perturbation theory, calculating response functions is difficult because it involves a huge number 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 developed to simulate the momentum-resolved spectrum probed by ARPES as well as core-level spectroscopies and neutron scattering. One important advantage of our approach is that it provides the spectrum directly in the frequency domain. Most previous approaches were based on the Fourier transform two-point correlation functions in time, a strategy that required filtering to resolve low-lying excitations. Our method has been applied to one-dimensional Mott insulators in and out-of-equilibrium using time-dependent Density Matrix Renormalization-Group (td-DMRG). A future perspective is to extend it to more general models (including 2D) and combine it with other numerical solvers. An interesting application of our approach that I intend to explore is inspired by a recent experimental study showing how to extract information about entanglement from the spin excitation spectrum.

Papers