Universal Features of Entanglement Entropy in the Honeycomb Hubbard Model

The entanglement entropy is a unique probe to access universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many basic universal features have yet to be observed. We show how to overcome this difficulty by introducing a new formulation to measure the Rényi entanglement entropy in auxiliary-field determinental quantum Monte Carlo simulations. In this framework, the entangling region itself becomes a stochastic variable. We demonstrate the precision and efficiency of this method by extracting, for the first time, universal logarithmic terms in a two dimensional model of interacting fermions. For this purpose we study the half-filled Hubbard model at T=0, where the universal corner term is detected throughout the semi-metal phase up to the Gross-Neveu-Yukawa critical point, and Goldstone modes are observed in the Mott insulating phase.