Entanglement Entropy of Interacting Fermions from Correlation functions

Entanglement measures such as entanglement entropy (EE) exhibit characteristic scaling behaviour with subsystem size in a variety of novel quantum states. However, analytical methods to calculate EE have been limited to non-interacting theories, or theories with conformal symmetry in one spatial dimension. Numerical methods applicable to more generic interacting systems can access small sizes limited by the exponentially growing computational complexity. Adapting recent Wigner-characteristic based techniques, we show that Renyi EE of interacting fermions in arbitrary dimensions can be represented as a Schwinger-Keldysh free energy on replicated manifolds with a current between the replicas. The current is local in real space and present only in the subsystem of interest. This lets us construct a diagrammatic representation of EE in terms of connected correlators in the standard unreplicated field theory. We further decompose EE into "particle" contributions which depend on the one-particle correlator, two-particle connected correlator and so on. For repulsively interacting fermions in two and three dimensions, we find the one particle contribution to entanglement picks up a leading volume scaling which is entirely determined by the incoherent piece of the one-particle momentum distribution function. The coefficient of the now subleading log-enhanced area piece is seen to decrease with increasing interaction strength.