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

In recent years entanglement measures, such as the von Neumann and the Rényi 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 Rényi entropies. The key idea is to perform a quench in the geometry of the replicas. The Rényi 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 Rényi entropies in the Ising universality class in 1+1 dimensions. We find perfect agreement with the well-known conformal field theory predictions.