# "Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological Phase"

**Speaker:**Cenke Xu , University of California - Santa Barbara

**When:**September 25, 2017 (Mon), 11:00AM to 12:30PM (add to my calendar)

**Location:**SCI 328

**Hosted by:**Anders Sandvik

*This event is part of the Condensed Matter Theory Seminar Series. *

We ask whether a local Hamiltonian with a featureless (fully gapped and nondegenerate) ground state could exist in certain quantum spin systems. We address this question by mapping the vicinity of certain quantum critical point (or gapless phase) of the dâˆ’dimensional spin system under study to the boundary of a (d+1)âˆ’dimensional bulk state, and the lattice symmetry of the spin system acts as an on-site symmetry in the field theory that describes both the selected critical point of the spin system, and the corresponding boundary state of the (d+1)âˆ’dimensional bulk. If the corresponding bulk state is a trivial state instead of a bosonic symmetry protected topological (SPT) state, then a featureless ground state of the spin system is allowed; if the corresponding bulk state is indeed a nontrivial SPT state, then it likely excludes the existence of a featureless ground state of the spin system. From this perspective we identify the spin systems with SU(N) and SO(N) symmetries on one, two and three dimensional lattices that permit a featureless ground state. We also verify our conclusions by other methods, including an explicit construction of these featureless spin states.