Entanglement Entropy from Nonequilibrium Work

The Rényi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field λ that controls the partition function topology, allowing us to define a notion of nonequilibrium work as λ is varied smoothly. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the Rényi entanglement entropy. We use these ideas to extract universal information from quantum Monte Carlo simulations of spin models in one and two dimensions. The vast gain in efficiency of this method allows us to access unprecedented system sizes up to 192×96 spins for the square lattice Heisenberg antiferromagnet.