  Symmetry-protected topological phases (SPTs) characterized by short-range
entanglement include many states essential to 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 intrinsic gapless SPTs through 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.
