Waveguide QED has emerged as a powerful analog quantum simulator due to the possibility of mediating versatile spin-spin interactions with tunable sign, range, and even dimerization. Yet, despite their potential, the many-body phases emerging from these systems have only been scarcely explored. Here, we characterize the many-body phases of a large class of spin models that can be obtained in such waveguide-QED simulators and uncover, importantly, the existence of symmetry-protected topological phases with large-period magnetic orderings with no analog in other state-of-art simulators. We explain that these phases emerge from the unique combination of long-range and dimerized interactions appearing in these platforms and propose several experimental observables to characterize them. Finally, we also develop an adiabatic protocol to prepare such states and analyze its performance with the main decoherence source of these systems.9 MoreReceived 30 June 2021Revised 24 January 2022Accepted 31 January 2022DOI:https://doi.org/10.1103/PRXQuantum.3.010336Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFrustrated magnetismPhase diagramsQuantum opticsSymmetry protected topological statesPhysical SystemsCollective dynamicsWaveguidesAtomic, Molecular & OpticalQuantum InformationCondensed Matter, Materials & Applied Physics