Topological Quantum Criticality from Multiplicative Topological Phases

Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to the understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential understanding of their consequences. In this work, we identify a fundamental connection between gapless SPTs and recently introduced multiplicative topological phases, demonstrating that multiplicative topological phases are an intuitive and general approach to realizing concrete models for gapless SPTs. In particular, they are naturally well suited to realizing higher-dimensional, stable, and intrinsically gapless SPTs through the combination of canonical topological insulator and semimetal models with critical gapless models in symmetry-protected tensor product constructions, opening avenues to far broader and deeper investigation of topology via short-range entanglement.