Cornering the universal entanglement of CFTs

Abstract

The structure of entanglement can yield new physical insights into strongly interacting quantum critical states. I’ll describe key properties of the entanglement entropy of conformal field theories (CFTs) in 2+1d. In particular, we’ll see that sharp corners in the entangling surface contribute a regulator-independent function that depends non-trivially on the corner angle. I’ll argue that in the smooth limit this function yields the 2-point function of the stress tensor. This sheds light on recent cutting edge simulations of the quantum critical Ising, XY and Heisenberg models. I’ll also present a new lower bound for this function. I will then generalize to Rényi entropies, which yields a simple procedure to extract the thermal entropy using corner entanglement of the groundstate alone. Connections will be made to CFTs in 1+1d and 3+1d, as well as to Lifshitz theories.