Laboratoire de Physique Théorique

de la Matière Condensée

Chunxiao Liu (UC Berkeley)

Lieb-Schultz-Mattis constraints in 3D: application to the pyrochlore and the diamond lattices

The Lieb-Schultz-Mattis (LSM) theorem is a powerful statement about when the lattice symmetry of a quantum magnet forbids a trivial paramagnetic ground state. Two formalisms of the theorem have been established: one uses the notation of lattice homotopy [Po et al., PRL 119, 127202 (2017)] and the other uses the idea of quantum anomalies [Else and Thorngren, PRB 101 224437, (2020)]. Here we discuss how these seemingly unrelated formalisms are unified, and how these ideas can be employed to obtain a set of complete LSM constraints in three-dimensional lattice magnets. We will focus on the LSM theorem on the pyrochlore, diamond, and breathing pyrochlore lattices, which host some of the prototypical spin liquids in three dimensions. We then go beyond the existing statement of the theorem by giving a detailed analysis of the microscopic origin of the LSM constraints. This analysis allows us to obtain and track the trivialization of the LSM constraints under the breaking of lattice symmetries. The principles and calculation methods presented in this work can be applied to all 3D lattice magnets.