Entanglement Entropy in Large-N Theories

Entanglement is one of the central concepts in quantum systems and is characterized by various moments of reduced density matrix, including Renyi and von Neumann entanglement entropies.



A large class of strongly correlated quantum systems can be described in certain large-N limits by actions that are quadratic in field and two-points functions which are determined by self-consistency equations. This includes both static and dynamic large-N description of Hubbard and Kondo lattice models as wells as Sachdev-Ye-Kitaev (SYK) models.



We develop a method to calculate the entanglement entropy of generic large-N theories, using the replica trick and the new notion of shifted Matsubara frequencies. Exact expressions are provided for the von Neumann and Renyi entanglement entropies, which in the non-interacting limit agree with existing results. Within this framework, however, the domain of applicability is extended to problems that include frequency-dependent self-energy, e.g. in presence of decoherence.



In the case of generic large-N interacting theories, our method reduces the computation of the entanglement entropy to numerical evaluation of a single determinant expressed entirely in terms of equilibrium spectral functions. As such, the knowledge of equilibrium solution is sufficient for computing the von Neumann entropy whereas Renyi entropy requires new solutions with modified boundary conditions. We illustrate the method by applying it to the coupled SYK model as a concrete example, in which low temperature emergence of entanglement has been casted recently in the context of holography.