Out-of-equilibrium protocol for Renyi entropies via the Jarzynski equality

In recent years entanglement measures, such as the von Neumann and the Renyi entropies, provided a unique opportunity to access elusive features of quantum many-body systems. However, extracting entanglement properties analytically, experimentally, or in numerical simulations can be a formidable task. Here, by combining the replica trick and the Jarzynski equality we devise an alternative effective out-of-equilibrium protocol for measuring the equilibrium Renyi entropies. The key idea is to perform a quench in the geometry of the replicas. The Renyi entropies are obtained as the exponential average of the work performed during the quench. We illustrate an application of the method in classical Monte Carlo simulations, although it could be useful in different contexts, such as in quantum Monte Carlo, or experimentally in cold-atom systems. The method is most effective in the quasistatic regime, i.e., for a slow quench. As a benchmark, we compute the Renyi entropies in the Ising universality class in 1 + 1 dimensions. We find perfect agreement with the well-known conformal field theory predictions.