Universal Features of Entanglement Entropy in the Honeycomb Hubbard Model.

The entanglement entropy is a unique probe to reveal 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 such universal features have yet to be observed. In this Letter we tackle this challenge by introducing a new method to compute the Rényi entanglement entropy in auxiliary-field quantum Monte Carlo simulations, where we treat the entangling region itself as a stochastic variable. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two-dimensional model of interacting fermions, focusing on the half-filled honeycomb Hubbard model at T=0. We detect the universal corner contribution due to gapless fermions throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, where the latter shows a pronounced enhancement depending on the type of entangling cut. Finally, we observe the universal Goldstone mode contribution in the antiferromagnetic Mott insulating phase.

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. This framework also naturally leads to the idea of using quench functions with spatially smooth profiles, providing us a way to average over lattice scale features of the entanglement entropy while preserving long distance universal information. We use these ideas to extract universal information from quantum Monte Carlo simulations of SU(N) 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.

New Easy-Plane CP

We study fixed points of the easy-plane CP^{N-1} field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU(N) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small N our lattice model has a first-order phase transition which progressively weakens as N increases, eventually becoming continuous for large values of N. Renormalization group calculations in 4-ε dimensions provide an explanation of these results as arising due to the existence of an N_{ep} that separates the fate of the flows with easy-plane anisotropy. When NN_{ep}, the flows are to a new easy-plane CP^{N-1} fixed point that describes the quantum criticality in the lattice model at large N. Our lattice model at its critical point, thus, gives efficient numerical access to a new strongly coupled gauge-matter field theory.