We consider the entanglement properties of ground states of Hamiltonians which are sums of commuting projectors (we call these commuting projector Hamiltonians), in particular whether or not they have “trivial” ground states, where a state is trivial if it is constructed by a local quantum circuit of bounded depth and range acting on a product state. It is known that Hamiltonians such as the to...

In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.

We present two new proofs of the the important q-commuting property holding among certain pairs of quantum minors of an n × n q-generic matrix. The first uses elementary quasideterminantal arithmetic; the second involves paths in an edge-weighted directed graph.

in this paper we introduce the construction of free profinite products of profinite groups withcommuting subgroups. we study a particular case: the proper free profinite products of profinite groups with commuting subgroups. we prove some conditions for a free profinite product of profinite groups with commuting subgroups to be proper. we derive some consequences. we also compute profinite comp...