My research is mainly concerned with Quantum Many-Body theory, Quantum Information, and Theoretical Condensed Matter. I am interested in showing how peculiar characteristics of quantum theory explain the observable behavior of many-body quantum systems. In particular, I am interested in the relaxation processes and degrade of information in quantum systems interacting with an environment and the theory of topological orders. They are both subjects in which the peculiarities of quantum theory are evident. Quantum information indeed degrades in a fundamentally different way than classical information, and topological orders in matter are not a classical order of the matter, but a quantum order. I am working on how to characterize topological orders using the most genuine characteristic of quantum theory, the entanglement.
Recently, I have been working on the topic of emergent gravity. The goal is to consider space-time dynamics as the effective theory of a quantum many-body system with simple degrees of freedom like a quantum spin network.
My most recent work is focused on the typicality of entanglement in physical states. Physical states are a tiny fraction of the Hilbert space of a quantum many body system. They are states that can be reached from a completely factored state by means of evolution with a local Hamiltonian for a polynomial time in the system size. I proved that these states are nearly maximal entangled. This has profound implications for the foundations of statistical mechanics.