  Topology in condensed matter physics is typically associated with a bulk
energy gap. However, recent research has shifted focus to topological phases
without a bulk energy gap, exhibiting nontrivial gapless topological behaviors.
In this letter, we explore a cluster Ising chain with long-range
antiferromagnetic interactions that decay as a power law with the distance.
Using complementary numerical and analytical techniques, we demonstrate that
long-range interactions can unambiguously induce an algebraic topological phase
and a topological Gaussian universality, both of which exhibit nontrivial
gapless topological behaviors. Our study not only provides a platform to
investigate the fundamental physics of quantum many-body systems but also
offers a novel route toward searching for gapless topological phases in
realistic quantum simulators.
