Lieb–Schultz–Mattis theorem for pyrochlore and diamond magnets

Chunxiao Liu (QuTech, TU Delft)

Lieb–Schultz–Mattis (LSM) theorem is a powerful statement about when the lattice symmetry of a quantum magnet forbids a trivial paramagnetic ground state. While a complete set of LSM theorems for 2D lattice magnets have been recently obtained, the LSM theorems for 3D lattice magnets have not been systematically studied. Here, motivated by the long standing problem of possible quantum spin liquids on the 3D pyrochlore and diamond lattices, we explicitly state the LSM theorem there, and show how the theorem precludes a trivial paramagnetic ground state for these lattices. Furthermore, we outline how a topological theory of the LSM theorem provides a selection rule on the possible types of quantum spin liquids, and how it allows us to obtain and track the stability of quantum spin liquids under the breaking of lattice symmetries. The principles and arguments presented here can be applied to all 3D lattice magnets.