Talk: Existence and stability in special cases of an area law in higher dimensions

Speaker: Andreas Bluhm

Abstract: We will review some known properties of gapped Hamiltonians on quantum spin systems. For those systems, it is conjectured that the entanglement entropy of ground states satisfies an area law. Based on a paper published by S. Michalakis in 2012, we will identify a condition under which we can prove an area law in dimensions d > 1. Furthermore, we will see that under the same condition the area law is stable under perturbations that do not close the spectral gap. Special attention will be paid to the role of the thermodynamic limit.