Laboratoire de Physique Théorique
Toulouse - UMR 5152

Spin is a fundamental property of quantum systems. Mathematically, it labels representations of the group SU(2). Inspired by success of gauge theories in high energy physics, we study generalized quantum condensed-matter systems : those of SU(N) symmetry with N > 2. Using the numerical framework of Tensor Networks, we construct SU(N)-symmetric wave functions and explore their physical properties. We show that paradigmatic wave functions such as those of the AKLT and the RVB states can be easily generalized to SU(N). Our goal is to find exotic phases such as topological quantum spin liquids, and to identify short-range Hamiltonians that realize them as the ground state.