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- Developing Tensor Network in mix representation: momentum/real-space mixing; as well encoding the TDVP in such framework. This in order to study interacting model in very nontrivial regime, as well as transport in the GHD framework and entanglement dynamics in momentum space.
- Full Counting Statistics out-of-equilibrium: inspecting time-dependent phase of matter; long-range interactions for long-range order at finite energy density.
- Tensor Network and Machine Learning: e.g. for quantum entanglement recognition.
- Lattice Gauge Theories (LGTs) in 1D and 2D via Tensor Network and Rydberg quantum simulator for 1D dynamics.
- Emerging confinement effects in quantum systems: from spin chains to LGTs; suppression of transport; disorder-free many-body localisation.
I am interested in the non-equilibrium dynamics of many-body quantum systems. I worked with both non-interacting and interacting (integrable or non-integrable) models. I have considerable expertise with numerical tools based on Tensor Network description of many-body quantum states: I dealt with developing MPS (for closed systems) and MPDO (for open system) with special attention to symmetries implementation and parallel optimization. Recently, I started to investigate how MPS, PEPS or Tree Tensor Networks may be proficiently applied in combination with Machine Learning techniques.
I am also an expert on a number of advanced toopics such as noninteracting quantum models, Thermodynamic Bethe Ansatz, entanglement entropies and quasi-particle picture. I have been always interested in developing new analytical and numerical methods or reformulating older ones in a more suitable way. This is important for the success of any project, which faces the limitations of the current analytical and numerical techniques.
I made several key contributions to these exciting areas of research and some of my works have become standard references: I developed a new framework for strongly interacting bosons to calculate the exact dynamics of correlation functions. I applied a semiclassical approach to characterise the dynamical confinement emerging in non-integrable spin chains. I implemented and enriched the numerical algorithms based on Matrix Product States in order to obtain an efficient description of quantum probability distribution functions of local observables. Recently, I developed (in collaboration with people from abroad) what is now known as “generalised hydrodynamics” (GHD): starting from a very simple physical picture, we have derived a continuity equation describing the late-time dynamics of inhomogeneous states in interacting integrable models.