Laboratoire de Physique Théorique
Toulouse - UMR 5152

In this talk, I will introduce two series of simple spin models with unusual properties. The first one is a modified Toric code that may have a unique ground state under periodic boundary condition, despite its nontrivial topological order dictated by nontrivial entanglement entropy and anyonic excitations. The second one is a spin chain in which a U(1) symmetry may be spontaneously broken at T=0, although naively such a phase is prohibited by the Hohenberg-Mermin-Wagner theorem. These examples will help our general understanding of quantum many-body systems and complete classification of possible phases of matter.