Entanglement Structure in Stoquastic Frustration Free Ground States

The well-known similarity transformation between the generators of Glauber dynamics for classical spin systems and quantum Hamiltonians gives rise to a variety of exactly solvable models without a sign problem, such as the quantum dimer model at the Rokhsar-Kivelson critical point. In this talk we describe a partial converse of this mapping, deriving sufficient conditions for stoquastic frustration free (SFF) ground states to be coherent classical Gibbs states with a local energy function. This leads to a decomposition of general SFF ground state entanglement into short-range contributions from the local energy function, and long-range entanglement from global constraints (such as conservation of parity or charge). From this perspective we can see the sign problem, and the associated phase frustration in the ground state wave function, is itself a primary mechanism for long-range entanglement in general quantum ground states.