Reduced density operators of finite-sized Heisenberg XXZ chains

In quantum many-body physics, reduced density operators play a central role in revealing the properties of a given system. We elaborate on this by studying finite size Heisenberg XXZ chains in the presence of periodic boundary conditions. As pointed out by F. Verstraete and J. Cirac, the admissible (2-site) local density matrices form a convex set determined by compatibility with translational invariance. The density matrices of ground states of translationally invariant nearest-neighbor Hamiltonians will define the boundary of this set. It is hard to determine this boundary without actually solving for many-body ground states, as knowledge of it would give immediate access to ground state energies of a rich class of models. Here we present studies on the size dependence of this mysterious boundary manifold. We also discuss non-analyticities of the boundary characterizing quantum phase transitions in the thermodynamic limit.