Lieb-Schultz-Mattis Theorem and the Filling Constraint

TL;DR

This paper extends the Lieb-Schultz-Mattis theorem to include magnetic and non-symmorphic lattice effects, linking anomalies to filling constraints and classifying crystalline quantum phases.

Contribution

It generalizes the topological classification of LSM anomalies to account for complex lattice symmetries and provides explicit calculations for specific systems.

Findings

Anomaly-free condition matches known filling constraints

Derived new filling constraints for crystalline systems

Connected LSM anomalies with topological phase classification

Abstract

Following recent developments in the classification of bosonic short-range entangled phases, we examine many-body quantum systems whose ground state fractionalization obeys the Lieb-Schultz-Mattis (LSM) theorem. We generalize the topological classification of such phases by LSM anomalies (arXiv:1907.08204) to take magnetic and non-symmorphic lattice effects into account, and provide direct computations of the LSM anomaly in specific examples. We show that the anomaly-free condition coincides with established filling constraints (arXiv:1705.09298, arXiv:1505.04193), and we also derived new ones on novel crystalline quantum systems.