Speaker
Description
We study gaplessness in one-dimensional quantum many-body systems with U(1) and translation symmetries under Lieb–Schultz–Mattis (LSM)–type constraints. While the LSM theorem imposes strong restrictions on the low-energy spectrum, the relation between charge- and neutral-excitations remains nontrivial in general interacting systems.
In this work, we show that, under physically reasonable conditions and in the presence of LSM-type constraints, the absence of a neutral gap implies the absence of a charge gap. Our approach is based on a dynamical construction using local twist operations combined with Lieb–Robinson bounds, which allows us to extract quasi-local excitations carrying finite quantum numbers with vanishing excitation energy.
Our results provide a unified perspective on gaplessness constrained by symmetry and filling, and suggest a general framework to diagnose gapless phases beyond specific models.