Entropia di entanglement da calcoli Monte Carlo fuori equilibrio

The study of entanglement in quantum systems is an important task in modern theoretical physics, since it is expected to reveal crucial features of the phase structure of strongly correlated quantum many-body systems and their quantum correlations. An observable that is widely used to quantify the amount of entanglement is the entanglement entropy, which can be calculated by means of the replica trick. However, explicit analytical results can be obtained only for systems with high level of symmetry, and even numerical calculations are still a formidable task. This motivates the search for efficient numerical algorithms to compute the entanglement entropy and related quantities that convey essentially the same information, such as Rényi entropies and the entropic c-function, by means of Monte Carlo calculations. In this thesis, after reviewing the main aspects of entanglement in quantum mechanics and quantum field theory, lattice theories, and their numerical simulation, we study a novel algorithm for the lattice calculation of Rényi entropies and the entropic c-function, which is based on Jarzynski’s equality: an exact theorem from non-equilibrium statistical mechanics. Our algorithm is validated against analytical results in the two-dimensional Ising model, then its generalization to the three-dimensional Ising model is discussed. Since the three-dimensional Ising model is dual to the Z2 gauge theory, this part of the work constitutes a new approach to the study of entanglement in these theories, bypassing the ambiguities affecting the definition of entanglement entropy in gauge theories. Finally, the results of this work will be summarized and their possible generalization to other physically interesting theories will be discussed.