My research activity is focused on the theoretical understanding of the role played by strong local correlations in low-dimensional many-body quantum systems, such as spin chains or fermionic/bosonic Hubbard-like models. These are believed to lie at the heart of many prominent aspects of quantum mechanics, including quantum phase transitions, high-temperature superconductivity, quantum magnetism, many-body localization, as well as topological order.

Despite the apparent simplicity of such systems, the lack of a dominant exactly solvable contribution limits the applicability of conventional perturbative methods, and restricts analytic studies to few cases. In high dimensionality mean-field approaches are often able to grasp the relevant features. In other circumstances approximated techniques as semiclassical theories or numerical approaches are an essential way out. I am an expert in numerical tools as exact diagonalization, quantum trajectories, and density-matrix renormalization group (DMRG).

I am dealing with different scenarios of the out-of-equilibrium quantum dynamics:

i) sudden quenches of closed systems, where abrupt variations of a Hamiltonian parameter induce a relaxation to a state which may locally behave as thermalized;

ii) slow quenches/annealing where, no matter how slow the parameters are varied, the presence of criticality unavoidably generates some defects;

iii) non-equilibrium physics in driven-dissipative systems, where the coupling to the environment may modify the two previous scenarios.

Besides the academic interest, these investigations have been recently boosted by the spectacular experimental advances in the realization and manipulation of “quantum simulators. Among them I am very interested in the physics of ultracold atomic gases trapped in optical lattices, as well as in dissipative arrays of coupled QED cavities. Fruitful discussions with experimentalists working on cold atoms loaded in optical lattices (e.g., at LENS in Florence), enabled me to understand the emergent peculiar behavior of quantum matter which is addressed in the lab. I quote the signatures of quantum Hall physics in ladder systems and the stabilization of persistent currents in presence of synthetic gauge fields, the dynamics of impurities and of spin entanglement in highly controllable scenarios. In the context of light-matter interaction, I am interested in characterizing arrays of coupled QED cavities, through models like the Jaynes-Cummings. Without dissipation, the system resembles the Bose-Hubbard physics for polaritonic dressed states. However the non-equilibrium conditions under which cavities naturally operate may lead to the appearance of new steady-state phases and novel paradigms for quantum criticality.

On a more fundamental level, I am exploring the many-body physics from a quantum information point of view. Spin chains are the prototype models, since the interplay between quantum correlations, phases of matter and entanglement develops in its fundamental aspects. Some of my contributions focus on zero-temperature quantum phase transitions, signaled by sudden changes of the ground-state properties, as long as the Hamiltonian parameters are varied. A valuable information is given by an information-theory analysis of quantum correlations (entanglement, quantum discord and related quantifiers), such as the relation between topological phases and entanglement spectrum properties. I am also working on the characterization of disordered many-body systems and on the appearance of a finite-temperature localization/delocalization transition. While this is framed in the context of the thermalization and ergodicity of closed systems, such behavior could be revealed by entropic indicators, as well as quantum information-like fidelity approaches.

I am a developer of algorithms for the simulation of many-body quantum systems, based on the reformulation of t-DMRG methods in the tensor network formalism. This approach follows the recent advances within the quantum information community, which introduced the notion of matrix product states (MPS), as well as the multiscale entanglement renormalization ansatz (MERA), and the projected entangled pair states (PEPS). I am working on the improvement of algorithms to study dissipative systems, and I would like to investigate the possibility to extend DMRG capabilities to address longer time scales and 2D systems, i.e., by integrating them with linked-cluster approaches.